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Volumn , Issue 294, 2004, Pages 27-62

Irrationalité de valeurs de zêta [d'après apéry, rivoal,...]

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EID: 33748741279     PISSN: 03031179     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Review
Times cited : (50)

References (118)
  • 1
    • 0034344445 scopus 로고    scopus 로고
    • A Gaussian hypergeometric series evaluation and Apéry number congruences
    • [AO]
    • [AO] S. AHLGREN &: K. ONO - «A Gaussian hypergeometric series evaluation and Apéry number congruences», J. reine angew. Math. 518 (2000), p. 187-212.
    • (2000) J. Reine Angew. Math. , vol.518 , pp. 187-212
    • Ahlgren, S.1    Ono, K.2
  • 2
    • 0033243811 scopus 로고    scopus 로고
    • Borwein and Bradley's Apéry-like formulae for ζ(4n + 3)
    • [AG]
    • [AG] G. ALMKVIST & A. GRANVILLE - «Borwein and Bradley's Apéry-like formulae for ζ(4n + 3)», Experiment. Math. 8 (1999), no. 2, p. 197-203.
    • (1999) Experiment. Math. , vol.8 , Issue.2 , pp. 197-203
    • Almkvist, G.1    Granville, A.2
  • 3
    • 0004244985 scopus 로고
    • [An], Aspects of Math., Vieweg
    • [An] Y. ANDRÉ - G-functions and geometry, Aspects of Math., vol. E13, Vieweg, 1989.
    • (1989) G-functions and Geometry , vol.E13
    • André, Y.1
  • 4
    • 0001052946 scopus 로고
    • Irrationalité de la somme des inverses de certaines suites réurrentes
    • [AnJ]
    • [AnJ] R. ANDRÉ-JEANNIN - «Irrationalité de la somme des inverses de certaines suites réurrentes», C. R. Acad. Sci. Paris Sér. I Math. 308 (1989), p. 539-541.
    • (1989) C. R. Acad. Sci. Paris Sér. I Math. , vol.308 , pp. 539-541
    • André-Jeannin, R.1
  • 5
    • 21744435831 scopus 로고    scopus 로고
    • The well-poised thread : An organized chronicle of some amazing summations and their implications
    • [And]
    • [And] G.E. ANDREWS - «The well-poised thread : an organized chronicle of some amazing summations and their implications», Ramanujan J. 1 (1997), no. 1, p. 7-23.
    • (1997) Ramanujan J. , vol.1 , Issue.1 , pp. 7-23
    • Andrews, G.E.1
  • 7
    • 0001934611 scopus 로고
    • Irrationalité de ζ(2) et ζ(3)
    • [Ap1], Astérisque, Société Mathématique de France
    • [Ap1] R. APÉRY - «Irrationalité de ζ(2) et ζ(3)», in Journées arithmétiques (Luminy, 1978), Astérisque, vol. 61, Société Mathématique de France, 1979, p. 11-13.
    • (1979) Journées Arithmétiques (Luminy, 1978) , vol.61 , pp. 11-13
    • Apéry, R.1
  • 9
    • 84974318061 scopus 로고
    • A recursive relation generalizing those of Apéry
    • [AW]
    • [AW] R. ASKEY & J.A. WILSON - «A recursive relation generalizing those of Apéry», J. Austral. Math. Soc. 36 (1984), p. 267-278.
    • (1984) J. Austral. Math. Soc. , vol.36 , pp. 267-278
    • Askey, R.1    Wilson, J.A.2
  • 10
    • 0011332881 scopus 로고    scopus 로고
    • Approximation theory and analytic number theory
    • [As], Allied Publishers, New Delhi
    • [As] W. VAN ASSCHE - «Approximation theory and analytic number theory», in Special Functions and Differential Equations (Madras, 1997), Allied Publishers, New Delhi, 1998, p. 336-355.
    • (1998) Special Functions and Differential Equations (Madras, 1997) , pp. 336-355
    • Van Assche, W.1
  • 11
    • 0035641769 scopus 로고    scopus 로고
    • Irrationalité d'une infinité de valeurs de la fonction zěta aux entiers impairs
    • [BR]
    • [BR] K.M. BALL.& T. RIVOAL - «Irrationalité d'une infinité de valeurs de la fonction zěta aux entiers impairs», Invent. Math. 140 (2001), p. 193-207.
    • (2001) Invent. Math. , vol.140 , pp. 193-207
    • Ball, K.M.1    Rivoal, T.2
  • 12
    • 33748743495 scopus 로고
    • Sur l'accélération de la convergence de certaines fractions continues
    • [BO], exp. no 23
    • [BO] C. BATUT & M. OLIVIER - «Sur l'accélération de la convergence de certaines fractions continues», in Sém. de Théorie des Nombres de Bordeaux 1979-1980, 1980, exp. no 23, 25 p.
    • (1980) Sém. de Théorie des Nombres de Bordeaux 1979-1980
    • Batut, C.1    Olivier, M.2
  • 13
    • 0000356657 scopus 로고
    • A note on the irrationality of ζ(2) and ζ(3)
    • [Be1]
    • [Be1] F. BEUKERS - «A note on the irrationality of ζ(2) and ζ(3)», Bull. London Math. Soc. 11 (1979), no. 3, p. 268-272.
    • (1979) Bull. London Math. Soc. , vol.11 , Issue.3 , pp. 268-272
    • Beukers, F.1
  • 14
    • 0001810624 scopus 로고
    • Padé-approximations in number theory
    • [Be2] _, Lect. Notes in Math., Springer, Berlin-New York
    • [Be2] _, «Padé-approximations in number theory», in Padé approximation and its applications, (Amsterdam, 1980), Lect. Notes in Math., vol. 888, Springer, Berlin-New York, 1981, p. 90-99.
    • (1981) Padé Approximation and Its Applications, (Amsterdam, 1980) , vol.888 , pp. 90-99
  • 15
    • 25944444172 scopus 로고
    • 1(5)
    • [Be3] _, (D. Bertrand & M. Waldschmidt, éds.), Progress in Math., Birkhäuser
    • 1(5)», in Approximations diophantiennes et nombres transcendants (Luminy, 1982) (D. Bertrand & M. Waldschmidt, éds.), Progress in Math., vol. 31, Birkhäuser, 1983, p. 47-66.
    • (1983) Approximations Diophantiennes et Nombres Transcendants (Luminy, 1982) , vol.31 , pp. 47-66
  • 16
    • 84859273224 scopus 로고
    • The values of polylogarithms
    • [Be4] _, Colloq. Math. Soc. János Bolyai
    • [Be4] _, «The values of polylogarithms», in Topics in classical number theory (Budapest, 1981), Colloq. Math. Soc. János Bolyai, vol. 34, 1984, p. 219-228.
    • (1984) Topics in Classical Number Theory (Budapest, 1981) , vol.34 , pp. 219-228
  • 17
    • 0002039277 scopus 로고
    • Some congruences for the Apéry numbers
    • [Be5] _
    • [Be5] _, «Some congruences for the Apéry numbers», J. Number Theory 21 (1985), p. 141-155.
    • (1985) J. Number Theory , vol.21 , pp. 141-155
  • 18
    • 14844366091 scopus 로고
    • Irrationality proofs using modular forms
    • [Be6] _, Astérisque, Société Mathématique de France
    • [Be6] _, «Irrationality proofs using modular forms», in Journées arithmétiques (Besançon, 1985), Astérisque, vol. 147-148, Société Mathématique de France, 1987, p. 271-283.
    • (1987) Journées Arithmétiques (Besançon, 1985) , vol.147-148 , pp. 271-283
  • 19
    • 38249037915 scopus 로고
    • Another congruence for the apéry numbers
    • [Be7] _
    • [Be7] _, «Another Congruence for the Apéry Numbers», J. Number Theory 25 (1987), p. 201-210.
    • (1987) J. Number Theory , vol.25 , pp. 201-210
  • 20
    • 0040817948 scopus 로고
    • A family of K3 surfaces and ζ(3)
    • [BP]
    • [BP] F. BEUKERS & C.A.M. PETERS - «A family of K3 surfaces and ζ(3)», J. reine angew. Math. 351 (1984), p. 42-54.
    • (1984) J. Reine Angew. Math. , vol.351 , pp. 42-54
    • Beukers, F.1    Peters, C.A.M.2
  • 21
    • 0031283914 scopus 로고    scopus 로고
    • Empirically determined Apéry-like formulae for ζ(4n + 3)
    • [BB]
    • [BB] J. BORWEIN & D. BRADLEY - «Empirically determined Apéry-like formulae for ζ(4n + 3)», Experiment. Math. 6 (1997), p. 181-194.
    • (1997) Experiment. Math. , vol.6 , pp. 181-194
    • Borwein, J.1    Bradley, D.2
  • 23
    • 0001261536 scopus 로고
    • Arithmetical investigations of a certain infinite product
    • [BV]
    • [BV] P. BUNDSCHUH & K. VÄÄNÄNEN - «Arithmetical investigations of a certain infinite product», Compositio Math. 91 (1994), p. 175-199.
    • (1994) Compositio Math. , vol.91 , pp. 175-199
    • Bundschuh, P.1    Väänänen, K.2
  • 24
    • 0002499459 scopus 로고
    • Démonstration automatique d'identités et fonctions hypergéométriques (d'après Zeilberger)
    • [Ca1], Astérisque, Société Mathématique de France, exp. no. 746
    • [Ca1] P. CARTIER - «Démonstration automatique d'identités et fonctions hypergéométriques (d'après Zeilberger)», in Sém. Bourbaki (1991/92), Astérisque, vol. 206, Société Mathématique de France, 1992, exp. no. 746, p. 41-91.
    • (1992) Sém. Bourbaki (1991/92) , vol.206 , pp. 41-91
    • Cartier, P.1
  • 25
    • 14844308752 scopus 로고    scopus 로고
    • Fonctions polylogarithmes, nombres polyzêtas et groupes prounipotents
    • [Ca2] _, Astérisque, Société Mathématique de France, exp. no. 885
    • [Ca2] _, «Fonctions polylogarithmes, nombres polyzêtas et groupes prounipotents», in Sém. Bourbaki (2000/01), Astérisque, vol. 282, Société Mathématique de France, 2002, exp. no. 885, p. 137-173.
    • (2002) Sém. Bourbaki (2000/01) , vol.282 , pp. 137-173
  • 26
    • 0039474242 scopus 로고
    • Congruence properties of Apéry numbers
    • [CCC]
    • [CCC] S. CHOWLA, J. COWLES & M. COWLES - «Congruence properties of Apéry numbers», J. Number Theory 12 (1980), p. 188-190.
    • (1980) J. Number Theory , vol.12 , pp. 188-190
    • Chowla, S.1    Cowles, J.2    Cowles, M.3
  • 28
    • 4243932438 scopus 로고
    • Démonstration de l'irrationalité do ζ(3) (d'après Apéry)
    • [Coh1], octobre
    • [Coh1] H. COHEN - «Démonstration de l'irrationalité do ζ(3) (d'après Apéry)», in Sém. de Théorie des Nombres de Grenoble, octobre 1978, 9 p.
    • (1978) Sém. de Théorie des Nombres de Grenoble
    • Cohen, H.1
  • 29
    • 14944349295 scopus 로고
    • Généralisation d'une construction de R. Apéry
    • [Coh2] _
    • [Coh2] _, «Généralisation d'une construction de R. Apéry», Bull. Soc. Math. France 109 (1981), p. 269-281.
    • (1981) Bull. Soc. Math. France , vol.109 , pp. 269-281
  • 30
    • 77952881730 scopus 로고    scopus 로고
    • Arithmétique de la fonction zêta
    • [Col], Journées X-UPS, Éditions de l'École polytechnique
    • [Col] P. COLMEZ - «Arithmétique de la fonction zêta», in La fonction zêta, Journées X-UPS, Éditions de l'École polytechnique, 2002.
    • (2002) La Fonction Zêta
    • Colmez, P.1
  • 33
    • 0013200006 scopus 로고
    • Arithmetic theory of differential equations
    • [Dw2] _, Academic Press
    • [Dw2] _, «Arithmetic theory of differential equations», in Symposia Math. (INDAM, Rome, 1979), vol. 24, Academic Press, 1981, p. 225-243.
    • (1981) Symposia Math. (INDAM, Rome, 1979) , vol.24 , pp. 225-243
  • 35
    • 33748751324 scopus 로고    scopus 로고
    • Transcendental numbers
    • [FN] (A.N. Parshin & I.R. Shafarevich, éds.), Encyclopaedia of Mathematical Sciences, Springer, Berlin
    • [FN] N.I. FEL'DMAN & YU.V. NESTERENKO - «Transcendental numbers», in Number theory, IV (A.N. Parshin & I.R. Shafarevich, éds.), Encyclopaedia of Mathematical Sciences, vol. 44, Springer, Berlin, 1998.
    • (1998) Number Theory, IV , vol.44
    • Fel'dman, N.I.1    Nesterenko, Yu.V.2
  • 36
    • 0038729551 scopus 로고    scopus 로고
    • Formes linéaires en polyzêtas et intégrales multiples
    • [Fi1]
    • [Fi1] S. FISCHLER - «Formes linéaires en polyzêtas et intégrales multiples», C. R. Acad. Sci. Paris Sér. I Math. 335 (2002), p. 1-4.
    • (2002) C. R. Acad. Sci. Paris Sér. I Math. , vol.335 , pp. 1-4
    • Fischler, S.1
  • 37
    • 85009837008 scopus 로고    scopus 로고
    • Groupes de Rhin-Viola et intégrales multiples
    • [Fi2] _
    • [Fi2] _, «Groupes de Rhin-Viola et intégrales multiples», J. Théor. Nombres Bordeaux 15 (2003), no. 2, p. 479-534.
    • (2003) J. Théor. Nombres Bordeaux , vol.15 , Issue.2 , pp. 479-534
  • 38
    • 0142087838 scopus 로고    scopus 로고
    • Approximants de Padé et séries hypergéomé triques équilibrées
    • [FR]
    • [FR] S. FISCHLER & T. RIVOAL - «Approximants de Padé et séries hypergéométriques équilibrées», J. Math. Pures Appl. 82 (2003), p. 1369-1394.
    • (2003) J. Math. Pures Appl. , vol.82 , pp. 1369-1394
    • Fischler, S.1    Rivoal, T.2
  • 40
    • 0002309719 scopus 로고
    • Some congruences for Apéry numbers
    • [Ges]
    • [Ges] I. GESSEL - «Some congruences for Apéry numbers», J. Number Theory 14 (1982), p. 362-368.
    • (1982) J. Number Theory , vol.14 , pp. 362-368
    • Gessel, I.1
  • 41
    • 14844346452 scopus 로고
    • The irrationality of certain quantities involving ζ(3)
    • [Gu1] [207]
    • [Gu1] L. A. GUTNIK - «The irrationality of certain quantities involving ζ(3)», Uspekhi Mat. Nauk 34 (1979), no. 3, 190 [207].
    • (1979) Uspekhi Mat. Nauk , vol.34 , Issue.3 , pp. 190
    • Gutnik, L.A.1
  • 42
    • 0000756817 scopus 로고
    • On the irrationality of some quantities containing ζ(3)
    • [Gu2] _, en russe
    • [Gu2] _, «On the irrationality of some quantities containing ζ(3)», Acta Arith. 42 (1983), no. 3, p. 255-264, en russe;
    • (1983) Acta Arith. , vol.42 , Issue.3 , pp. 255-264
  • 43
    • 0002162396 scopus 로고
    • traduction en anglais dans
    • traduction en anglais dans Amer. Math. Soc. Transl., 140 (1988), p. 45-55.
    • (1988) Amer. Math. Soc. Transl. , vol.140 , pp. 45-55
  • 46
    • 0000186632 scopus 로고
    • On the linear independence of the values of polylogarithmic functions
    • [Hat1]
    • [Hat1] M. HATA - «On the linear independence of the values of polylogarithmic functions», J. Math. Pures Appl. 69 (1990), no. 2, p. 133-173.
    • (1990) J. Math. Pures Appl. , vol.69 , Issue.2 , pp. 133-173
    • Hata, M.1
  • 47
    • 84968476256 scopus 로고
    • Rational approximations to the dilogarithm
    • [Hat2] _
    • [Hat2] _, «Rational approximations to the dilogarithm», Trans. Amer. Math. Soc. 336 (1993), no. 1, p. 363-387.
    • (1993) Trans. Amer. Math. Soc. , vol.336 , Issue.1 , pp. 363-387
  • 48
    • 0034366259 scopus 로고    scopus 로고
    • A new irrationality measure for ζ(3)
    • [Hat3] _
    • [Hat3] _, «A new irrationality measure for ζ(3)», Acta Arith. 92 (2000), no. 1, p. 47-57.
    • (2000) Acta Arith. , vol.92 , Issue.1 , pp. 47-57
  • 49
    • 0004206239 scopus 로고
    • [Haz], Pure and Applied Mathematics, Academic Press
    • [Haz] M. HAZEWINKEL - Formal groups and applications, Pure and Applied Mathematics, vol. 78, Academic Press, 1978.
    • (1978) Formal Groups and Applications , vol.78
    • Hazewinkel, M.1
  • 50
    • 33747430511 scopus 로고    scopus 로고
    • Linear independence of vectors with polylogarithmic coordinates
    • [He]
    • [He] T.G. HESSAMI PILEHROOD - «Linear independence of vectors with polylogarithmic coordinates», Vestnik Moskov. Univ. Ser. I Mat. Mekh. 54 (1999), no. 6, p. 54-56,
    • (1999) Vestnik Moskov. Univ. Ser. I Mat. Mekh. , vol.54 , Issue.6 , pp. 54-56
    • Hessami Pilehrood, T.G.1
  • 52
    • 85009836191 scopus 로고    scopus 로고
    • Équations différentielles fuchsiennes. Approximations du dilogarithme, de ζ(2) et de ζ(3)
    • [Hu1]
    • [Hu1] M. HUTTNER - «Équations différentielles fuchsiennes. Approximations du dilogarithme, de ζ(2) et de ζ(3)», Pub. IRMA Lille 43 (1997).
    • (1997) Pub. IRMA Lille , vol.43
    • Huttner, M.1
  • 53
    • 0142065367 scopus 로고    scopus 로고
    • Constructible sets of linear differential equations and effective rational approximations of G-functions
    • [Hu2] _
    • [Hu2] _, «Constructible sets of linear differential equations and effective rational approximations of G-functions», Pub. IRMA Lille 59 (2002).
    • (2002) Pub. IRMA Lille , vol.59
  • 56
    • 0002234445 scopus 로고
    • On Beukers' conjecture
    • [Is]
    • [Is] T. ISIIIKAWA - «On Beukers' conjecture», Kobe J. Math. 6 (1989), p. 49-52.
    • (1989) Kobe J. Math. , vol.6 , pp. 49-52
    • Isiiikawa, T.1
  • 58
    • 33748755487 scopus 로고    scopus 로고
    • [Kr] Communication personnelle du 28 octobre
    • [Kr] C. KRATTENTHALER - Communication personnelle du 28 octobre 2002.
    • (2002)
    • Krattenthaler, C.1
  • 59
    • 0003956970 scopus 로고
    • [La], Addison-Wesley
    • e éd., Addison-Wesley, 1993.
    • (1993) e Éd.
    • Lang, S.1
  • 60
    • 4243737968 scopus 로고
    • Some new identities for ζ(k)
    • [Le]
    • [Le] D. LESHCHINER - «Some new identities for ζ(k)», J. Number Theory 13 (1981), p. 355-362.
    • (1981) J. Number Theory , vol.13 , pp. 355-362
    • Leshchiner, D.1
  • 61
    • 0041155681 scopus 로고
    • Sur des classes très étendues de quantités dont la valeur n'est ni algébrique, ni même réductible à des irrationnelles algébriques
    • [Li]
    • [Li] J. LIOUVILLE - «Sur des classes très étendues de quantités dont la valeur n'est ni algébrique, ni même réductible à des irrationnelles algébriques», J. Math. Pures Appl. 16 (1851), p. 133-142.
    • (1851) J. Math. Pures Appl. , vol.16 , pp. 133-142
    • Liouville, J.1
  • 62
    • 0003783929 scopus 로고
    • [Lu], Mathematics in Science and Engineering, Academic Press
    • [Lu] Y.L. LUKE - The special functions and their approximations, vol. I, Mathematics in Science and Engineering, vol. 53, Academic Press, 1969.
    • (1969) The Special Functions and Their Approximations , vol.1
    • Luke, Y.L.1
  • 63
    • 84859289992 scopus 로고
    • Roger Apéry et l'irrationnel
    • [Me]
    • [Me] M. MENDÈS-FRANCE - «Roger Apéry et l'irrationnel», La Recherche 97 (1979), p. 170-172.
    • (1979) La Recherche , vol.97 , pp. 170-172
    • Mendès-France, M.1
  • 64
  • 66
    • 0001423294 scopus 로고    scopus 로고
    • A few remarks on ζ(3)
    • [Ne2] _
    • [Ne2] _, «A few remarks on ζ(3)», Mat. Zametki 59 (1996), no. 6, p. 865-880,
    • (1996) Mat. Zametki , vol.59 , Issue.6 , pp. 865-880
  • 67
    • 0007085336 scopus 로고    scopus 로고
    • Math. Notes, p. 625-636.
    • Math. Notes , pp. 625-636
  • 68
    • 85009885066 scopus 로고    scopus 로고
    • Integral identities and constructions of approximations to zeta-values
    • [Ne3] _
    • [Ne3] _, «Integral identities and constructions of approximations to zeta-values», J. Théor. Nombres Bordeaux 15 (2003), no. 2, p. 535-550.
    • (2003) J. Théor. Nombres Bordeaux , vol.15 , Issue.2 , pp. 535-550
  • 69
    • 0000023788 scopus 로고
    • On the irrationality of the values of the functions F(x,s)
    • [Ni]
    • [Ni] E.M. NIKISHIN - «On the irrationality of the values of the functions F(x,s)», Mat. Sbornik 109 (1979), no. 3, p. 410-417,
    • (1979) Mat. Sbornik , vol.109 , Issue.3 , pp. 410-417
    • Nikishin, E.M.1
  • 70
    • 84957167586 scopus 로고    scopus 로고
    • Math. USSR-Sb. 37, p. 381-388.
    • Math. USSR-Sb. , vol.37 , pp. 381-388
  • 73
    • 0039797800 scopus 로고
    • Polylogarithmes
    • [Oe], Astérisque, Société Mathématique de France, exp. no 762
    • [Oe] J. OESTERLÉ - «Polylogarithmes», in Sém. Bourbaki (1992/93), Astérisque, vol. 216, Société Mathématique de France, 1993, exp. no 762, p. 49-67.
    • (1993) Sém. Bourbaki (1992/93) , vol.216 , pp. 49-67
    • Oesterlé, J.1
  • 74
    • 0000968547 scopus 로고
    • A pencil of K3-surfaces related to Apéry's recurrence for ζ(3) and Fermi surfaces for potential zero
    • [PS] (W.P. Barth & H. Lange, éds.), Lect. Notes in Math., Springer
    • [PS] C. PETERS & J. STIENSTRA - «A pencil of K3-surfaces related to Apéry's recurrence for ζ(3) and Fermi surfaces for potential zero», in Arithmetics of complex manifolds (Erlangen, 1988) (W.P. Barth & H. Lange, éds.), Lect. Notes in Math., vol. 1399, Springer, 1989, p. 110-127.
    • (1989) Arithmetics of Complex Manifolds (Erlangen, 1988) , vol.1399 , pp. 110-127
    • Peters, C.1    Stienstra, J.2
  • 76
    • 0002145526 scopus 로고
    • A proof that Euler missed... Apéry's proof of the irrationality of ζ(3)
    • [Po1]
    • [Po1] A. VAN DER POORTEN - «A proof that Euler missed... Apéry's proof of the irrationality of ζ(3)», Math. Intelligencer I (1978-79), no. 4, p. 195-203.
    • (1978) Math. Intelligencer , vol.1 , Issue.4 , pp. 195-203
    • Van Der Poorten, A.1
  • 77
    • 84859288601 scopus 로고
    • Some wonderful formulae... footnotes to Apéry's proof of the irrationality of ζ(3)
    • [Po2] _, exp. 29
    • e année, 1978-79, exp. 29, 7 p.
    • (1978) e Année
  • 78
    • 0009323649 scopus 로고
    • Some wonderful formulas... an introduction to polylogarithms
    • [Po3] _, Queen's Papers in Pure and Applied Mathematics
    • [Po3] _, «Some wonderful formulas... an introduction to polylogarithms», in Proceedings of the Queen's Number Theory Conference (Kingston, 1979), Queen's Papers in Pure and Applied Mathematics, vol. 54, 1980, p. 269-286.
    • (1980) Proceedings of the Queen's Number Theory Conference (Kingston, 1979) , vol.54 , pp. 269-286
  • 79
    • 0030102978 scopus 로고    scopus 로고
    • A new proof of the irrationality of ζ(2) and ζ(3) using Padé approximants
    • [Pr1]
    • [Pr1] M. PRéVOST - «A new proof of the irrationality of ζ(2) and ζ(3) using Padé approximants», J. Comp. Appl. Math. 67 (1996), p. 219-235.
    • (1996) J. Comp. Appl. Math. , vol.67 , pp. 219-235
    • Prévost, M.1
  • 80
    • 0002573342 scopus 로고    scopus 로고
    • n
    • [Pr2] _
    • n», J. Number Theory 73 (1998), p. 139-161.
    • (1998) J. Number Theory , vol.73 , pp. 139-161
  • 81
    • 84859278133 scopus 로고
    • Irrationalité de ζ(3) selon Apéry
    • [Re1], exp. 6
    • e année, 1978-79, exp. 6, 6 p.
    • (1978) e Année
    • Reyssat, E.1
  • 82
    • 33748756473 scopus 로고
    • Mesures de transcendance pour les logarithmes de nombres rationnels
    • [Re2] _, (D. Bertrand & M. Waldschmidt, éds.), Progress in Math., Birkhäuser
    • [Re2] _, «Mesures de transcendance pour les logarithmes de nombres rationnels», in Approximations diophantiennes et nombres transcendants (Luminy, 1982) (D. Bertrand & M. Waldschmidt, éds.), Progress in Math., vol. 31, Birkhäuser, 1983, p. 235-245.
    • (1983) Approximations Diophantiennes et Nombres Transcendants (Luminy, 1982) , vol.31 , pp. 235-245
  • 83
    • 0035651903 scopus 로고    scopus 로고
    • The group structure for ζ(3)
    • [RV]
    • [RV] G. RHIN & C. VIOLA - «The group structure for ζ(3)», Acta Arith. 97 (2001), no. 3, p. 269-293.
    • (2001) Acta Arith. , vol.97 , Issue.3 , pp. 269-293
    • Rhin, G.1    Viola, C.2
  • 84
    • 0034662540 scopus 로고    scopus 로고
    • La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs
    • [Ri1]
    • [Ri1] T. RIVOAL - «La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs», C. R. Acad. Sci. Paris Sér. I Math. 331 (2000), no. 4, p. 267-270.
    • (2000) C. R. Acad. Sci. Paris Sér. I Math. , vol.331 , Issue.4 , pp. 267-270
    • Rivoal, T.1
  • 86
    • 0042762688 scopus 로고    scopus 로고
    • Irrationalité d'au moins un des neuf nombres ζ(5), ζ(7),..., ζ(21)
    • [Ri3] _
    • [Ri3] _, «Irrationalité d'au moins un des neuf nombres ζ(5), ζ(7),..., ζ(21)», Acta Arith. 103 (2002), no. 2, p. 157-167.
    • (2002) Acta Arith. , vol.103 , Issue.2 , pp. 157-167
  • 87
    • 85009833805 scopus 로고    scopus 로고
    • Séries hypcrgéométriques et irrationalité des valeurs de la fonction zěta de Riemann
    • [Ri4] _
    • [Ri4] _, «Séries hypcrgéométriques et irrationalité des valeurs de la fonction zěta de Riemann», J. Théor. Nombres Bordeaux 15 (2003), no. 1, p. 351-365.
    • (2003) J. Théor. Nombres Bordeaux , vol.15 , Issue.1 , pp. 351-365
  • 88
    • 0041917212 scopus 로고    scopus 로고
    • Diophantine properties of numbers related to Catalan's constant
    • [RZ]
    • [RZ] T. RIVOAL & W. ZUDILIN - «Diophantine properties of numbers related to Catalan's constant», Math. Annalen 326 (2003), p. 705-721.
    • (2003) Math. Annalen , vol.326 , pp. 705-721
    • Rivoal, T.1    Zudilin, W.2
  • 89
    • 0003996349 scopus 로고
    • [Se], Presses Universitaires de France
    • [Se] J.-P. SERRE - Cours d'arithmétique, Presses Universitaires de France, 1970.
    • (1970) Cours d'Arithmétique
    • Serre, J.-P.1
  • 91
    • 0002081353 scopus 로고
    • Hermite-Padé approximations for Nikishin systems and the irrationality of ζ(3)
    • [Sol]
    • [Sol] V.N. SOROKIN - «Hermite-Padé approximations for Nikishin systems and the irrationality of ζ(3)», Uspekhi Mat. Nauk 49 (1994), no. 2, p. 167-168,
    • (1994) Uspekhi Mat. Nauk , vol.49 , Issue.2 , pp. 167-168
    • Sorokin, V.N.1
  • 93
    • 0001811025 scopus 로고
    • A transcendence measure for π2
    • [So2] _
    • [So2] _, «A transcendence measure for π2», Mat. Sbornik 187 (1990), no. 12, p; 87-120,
    • (1990) Mat. Sbornik , vol.187 , Issue.12 , pp. 87-120
  • 94
    • 33748744826 scopus 로고    scopus 로고
    • Sb. Math., p. 1819-1852.
    • Sb. Math. , pp. 1819-1852
  • 95
    • 0038583254 scopus 로고    scopus 로고
    • Apery's theorem
    • [So3] _
    • [So3] _, «Apery's theorem», Vestnik Moskov. Univ. Ser. I Mat. Mekh. 53 (1998), no. 3, p. 48-53,
    • (1998) Vestnik Moskov. Univ. Ser. I Mat. Mekh. , vol.53 , Issue.3 , pp. 48-53
  • 97
    • 0001315940 scopus 로고
    • On the Picard-Fuchs equation and the formal Brauer group of certain elliptic K3-surfaces
    • [SB]
    • [SB] J. STIENSTRA & F. BEUKERS - «On the Picard-Fuchs equation and the formal Brauer group of certain elliptic K3-surfaces», Math. Ann. 271 (1985), p. 269-304.
    • (1985) Math. Ann. , vol.271 , pp. 269-304
    • Stienstra, J.1    Beukers, F.2
  • 98
    • 0040682067 scopus 로고    scopus 로고
    • On a conjecture of Chowla et al.
    • [Su]
    • [Su] B. SURY - «On a conjecture of Chowla et al.», J. Number Theory 72 (1998), p. 137-139.
    • (1998) J. Number Theory , vol.72 , pp. 137-139
    • Sury, B.1
  • 100
    • 9944254696 scopus 로고    scopus 로고
    • Some formulas for Riemann zeta-function at integer points
    • [Va1]
    • [Va1] D.V. VASILYEV - «Some formulas for Riemann zeta-function at integer points», Vestnik Moskov. Univ. Ser. I Mat. Mekh. 51 (1996), no. 1, p. 81-84,
    • (1996) Vestnik Moskov. Univ. Ser. I Mat. Mekh. , vol.51 , Issue.1 , pp. 81-84
    • Vasilyev, D.V.1
  • 102
    • 0012232945 scopus 로고    scopus 로고
    • On small linear forms for the values of the Riemann zeta-function at odd integers
    • [Va2] _, en russe
    • [Va2] _, «On small linear forms for the values of the Riemann zeta-function at odd integers», Doklady NAN Belarusi (Reports of the Belarus National Academy of Sciences) 45 (2001), no. 5, p. 36-40, en russe.
    • (2001) Doklady NAN Belarusi (Reports of the Belarus National Academy of Sciences) , vol.45 , Issue.5 , pp. 36-40
  • 103
    • 85009910356 scopus 로고    scopus 로고
    • Valeurs zêta multiples: Une introduction
    • [Wa]
    • [Wa] M. WALDSCHMIDT - «Valeurs zêta multiples: une introduction», J. Théor. Nombres Bordeaux 12 (2000), p. 581-595.
    • (2000) J. Théor. Nombres Bordeaux , vol.12 , pp. 581-595
    • Waldschmidt, M.1
  • 104
    • 84859274848 scopus 로고
    • Remarks on Hecke's lemma and its use
    • [We], Springer
    • [We] A. WEIL - «Remarks on Hecke's lemma and its use», in Œuvres scientifiques - Collected Papers III, Springer, 1979, p. 405-412.
    • (1979) ŒUvres Scientifiques - Collected Papers III , pp. 405-412
    • Weil, A.1
  • 106
    • 0002556812 scopus 로고
    • Introduction to modular forms
    • [Za1] (M. Waldschmidt, p. Moussa, J.M. Luck & C. Itzykson, éds.), Springer
    • [Za1] D. ZAGIER - «Introduction to modular forms», in From number theory to physics (Les Hauches, 1989) (M. Waldschmidt, p. Moussa, J.M. Luck & C. Itzykson, éds.), Springer, 1992, p. 238-291.
    • (1992) From Number Theory to Physics (Les Hauches, 1989) , pp. 238-291
    • Zagier, D.1
  • 108
    • 0001372251 scopus 로고
    • Closed form (pun intended !)
    • [Ze1] (M. Knopp &; M. Sheingorn, éds.), Comtemporary Math., American Mathematical Society
    • [Ze1] D. ZEILBERGER - «Closed form (pun intended !)», in A tribute to Emil Gross-wald: Number theory and related analysis (M. Knopp &; M. Sheingorn, éds.), Comtemporary Math., vol. 143, American Mathematical Society, 1993, p. 579-607.
    • (1993) A Tribute to Emil Gross-wald: Number Theory and Related Analysis , vol.143 , pp. 579-607
    • Zeilberger, D.1
  • 109
    • 33748750860 scopus 로고    scopus 로고
    • Computerized deconstruction
    • [Ze2] _
    • [Ze2] _, «Computerized deconstruction», Adv. Applied Math. 31 (2003), p. 532-543.
    • (2003) Adv. Applied Math. , vol.31 , pp. 532-543
  • 110
    • 0000736689 scopus 로고    scopus 로고
    • Integrals expressible as linear forms in generalized polylogarithms
    • [Zl]
    • [Zl] S.A. ZLOBIN - «Integrals expressible as linear forms in generalized polylogarithms», Mat. Zametki 71 (2002), no. 5, p. 782-787,
    • (2002) Mat. Zametki , vol.71 , Issue.5 , pp. 782-787
    • Zlobin, S.A.1
  • 111
    • 0007085336 scopus 로고    scopus 로고
    • Math. Notes, p. 711-716.
    • Math. Notes , pp. 711-716
  • 112
    • 0042753428 scopus 로고    scopus 로고
    • One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational
    • [Zu1]
    • [Zu1] W. ZUDILIN - «One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational», Uspekhi Mat. Nauk 56 (2001), no. 4, p. 149-150,
    • (2001) Uspekhi Mat. Nauk , vol.56 , Issue.4 , pp. 149-150
    • Zudilin, W.1
  • 114
    • 0012232310 scopus 로고    scopus 로고
    • Irrationality of values of the Riemann zeta function
    • [Zu2] _
    • [Zu2] _, «Irrationality of values of the Riemann zeta function», Izvestiya RAN Ser. Mat. 66 (2002), no. 3, p. 49-102,
    • (2002) Izvestiya RAN Ser. Mat. , vol.66 , Issue.3 , pp. 49-102
  • 115
    • 33748749663 scopus 로고    scopus 로고
    • Izv. Math., p. 489-542.
    • Izv. Math. , pp. 489-542
  • 116
    • 85009876001 scopus 로고    scopus 로고
    • Well-poised hypergeometric service for diophnntine problems of zeta values
    • [Zu3] _
    • [Zu3] _, «Well-poised hypergeometric service for diophnntine problems of zeta values», J. Théor. Nombres Bordeaux 15 (2003), no. 2, p. 593-626.
    • (2003) J. Théor. Nombres Bordeaux , vol.15 , Issue.2 , pp. 593-626


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