메뉴 건너뛰기




Volumn 66, Issue 3, 2002, Pages 489-542

Irrationality of values of the Riemann zeta function

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0013122681     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM2002v066n03ABEH000387     Document Type: Article
Times cited : (26)

References (39)
  • 1
    • 0001934611 scopus 로고
    • Irrationalité de ζ(2) et ζ(3)
    • R. Apéry, "Irrationalité de ζ(2) et ζ(3)", Astérisque 61 (1979), 11-13.
    • (1979) Astérisque , vol.61 , pp. 11-13
    • Apéry, R.1
  • 2
    • 0002145526 scopus 로고
    • A proof that Euler missed... Apéry's proof of the irrationality of ζ(3). An informal report
    • A. van der Poorten, "A proof that Euler missed... Apéry's proof of the irrationality of ζ(3). An informal report", Math. Intelligencer 1:4 (1978/79), 195-203.
    • (1978) Math. Intelligencer , vol.1 , Issue.4 , pp. 195-203
    • Van Der Poorten, A.1
  • 3
    • 0000356657 scopus 로고
    • A note on the irrationality of ζ(2) and ζ(3)
    • F. Beukers, "A note on the irrationality of ζ(2) and ζ(3)", Dull. London Math. Soc. 11 (1979), 268-272.
    • (1979) Dull. London Math. Soc. , vol.11 , pp. 268-272
    • Beukers, F.1
  • 4
    • 14844346452 scopus 로고
    • The irrationality of certain quantities involving ζ(3)
    • L.A. Gutnik, "The irrationality of certain quantities involving ζ(3)", Uspekhi Mat. Nauk 34:3 (1979), 190;
    • (1979) Uspekhi Mat. Nauk , vol.34 , Issue.3 , pp. 190
    • Gutnik, L.A.1
  • 5
    • 33748560222 scopus 로고
    • English transl., Russian Math. Surveys 34:3 (1979), 200;
    • (1979) Russian Math. Surveys , vol.34 , Issue.3 , pp. 200
  • 6
    • 0000756817 scopus 로고
    • Acta Arith. 42:3 (1983), 255-264.
    • (1983) Acta Arith. , vol.42 , Issue.3 , pp. 255-264
  • 7
    • 0001810624 scopus 로고
    • Padé approximations in number theory
    • Springer-Verlag, Berlin
    • F. Beukers, "Padé approximations in number theory", Lecture Notes in Math., vol. 888, Springer-Verlag, Berlin 1981, pp. 90-99.
    • (1981) Lecture Notes in Math. , vol.888 , pp. 90-99
    • Beukers, F.1
  • 8
    • 14844366091 scopus 로고
    • Irrationality proofs using modular forms
    • F. Beukers, "Irrationality proofs using modular forms", Astérisque 147-148 (1987), 271-283.
    • (1987) Astérisque , vol.147-148 , pp. 271-283
    • Beukers, F.1
  • 9
    • 0002081353 scopus 로고
    • Hermite-Padé approximations of Nikishin systems and the irrationality of ζ(3)
    • V. N. Sorokin, "Hermite-Padé approximations of Nikishin systems and the irrationality of ζ(3)", Uspekhi Mat. Nauk 49:2 (1994), 167-168;
    • (1994) Uspekhi Mat. Nauk , vol.49 , Issue.2 , pp. 167-168
    • Sorokin, V.N.1
  • 10
    • 85164642758 scopus 로고
    • English transl., Russian Math. Surveys 49:2 (1991), 176-177.
    • (1991) Russian Math. Surveys , vol.49 , Issue.2 , pp. 176-177
  • 11
    • 0001423294 scopus 로고    scopus 로고
    • A few remarks on ζ(3)
    • Yu. V. Nesterenko, "A few remarks on ζ(3)", Mat. Zametki 59 (1996), 865-880;
    • (1996) Mat. Zametki , vol.59 , pp. 865-880
    • Nesterenko, Yu.V.1
  • 12
    • 0001720123 scopus 로고    scopus 로고
    • English transl., Math. Notes 59 (1996), 625-636.
    • (1996) Math. Notes , vol.59 , pp. 625-636
  • 13
    • 0034366259 scopus 로고    scopus 로고
    • A new irrationality measure for ζ(3)
    • M. Hata, "A new irrationality measure for ζ(3)", Acta Arith. 92:1 (2000), 47-57.
    • (2000) Acta Arith. , vol.92 , Issue.1 , pp. 47-57
    • Hata, M.1
  • 14
    • 0035651903 scopus 로고    scopus 로고
    • The group structure for ζ(3)
    • G. Rhin and C. Viola, "The group structure for ζ(3)", Acta Arith. 97:3 (2001), 269-293.
    • (2001) Acta Arith. , vol.97 , Issue.3 , pp. 269-293
    • Rhin, G.1    Viola, C.2
  • 17
    • 0034662540 scopus 로고    scopus 로고
    • La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs
    • T. Rivoal, "La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs", C. R. Acad. Sci. Paris Sér. I Math. 331:4 (2000), 267-270; http://arXiv.org/abs/ math/0008051.
    • (2000) C. R. Acad. Sci. Paris Sér. I Math. , vol.331 , Issue.4 , pp. 267-270
    • Rivoal, T.1
  • 19
    • 0035641769 scopus 로고    scopus 로고
    • Irrationalité d'une infinité de valeurs de la fonction zêta aux entiers impairs
    • K. Ball and T. Rivoal, "Irrationalité d'une infinité de valeurs de la fonction zêta aux entiers impairs", Invent. Math. 146:1 (2001), 193-207.
    • (2001) Invent. Math. , vol.146 , Issue.1 , pp. 193-207
    • Ball, K.1    Rivoal, T.2
  • 21
    • 0039882582 scopus 로고
    • English transl., Moscow Univ. Math. Bull. 40:1 (1985), 69-74.
    • (1985) Moscow Univ. Math. Bull. , vol.40 , Issue.1 , pp. 69-74
  • 23
    • 33747430511 scopus 로고    scopus 로고
    • Linear independence of vectors with polylogarithmic coordinates
    • "Linear independence of vectors with polylogarithmic coordinates", Vestnik Moskov. Univ. Ser. 1 Mat. Mekh. 1999, no. 6, 54-56;
    • (1999) Vestnik Moskov. Univ. Ser. 1 Mat. Mekh. , Issue.6 , pp. 54-56
  • 24
    • 85164653175 scopus 로고    scopus 로고
    • English transl., Moscow Univ. Math. Bull. 54:6 (1999), 40-42
    • (1999) Moscow Univ. Math. Bull. , vol.54 , Issue.6 , pp. 40-42
  • 25
    • 0012446789 scopus 로고
    • A lower estimate for rational approximations of in 2
    • E. A. Rukhadze, "A lower estimate for rational approximations of In 2", Vestnik Moskov. Univ. Ser. 1 Mat. Mekh. 1987, no. 6, 25-29;
    • (1987) Vestnik Moskov. Univ. Ser. 1 Mat. Mekh. , Issue.6 , pp. 25-29
    • Rukhadze, E.A.1
  • 26
    • 85164654255 scopus 로고
    • English transl., Moscow Univ. Math. Bull. 42:6 (1987), 30-35.
    • (1987) Moscow Univ. Math. Bull. , vol.42 , Issue.6 , pp. 30-35
  • 27
    • 0005232525 scopus 로고    scopus 로고
    • On the irrationality of the values of the zeta function at odd integer points
    • V. V. Zudilin, "On the irrationality of the values of the zeta function at odd integer points"', Uspekhi Mat. Nauk 56:2 (2001), 215-216;
    • (2001) Uspekhi Mat. Nauk , vol.56 , Issue.2 , pp. 215-216
    • Zudilin, V.V.1
  • 28
    • 0035594959 scopus 로고    scopus 로고
    • English transl., Russian Math. Surveys 56 (2001), 423-424.
    • (2001) Russian Math. Surveys , vol.56 , pp. 423-424
  • 29
    • 0000023788 scopus 로고
    • On the irrationality of the values of the functions F(x, s)
    • E. M. Nikishin, "On the irrationality of the values of the functions F(x, s)", Mat. Sbornik 109 (1979), 410-417;
    • (1979) Mat. Sbornik , vol.109 , pp. 410-417
    • Nikishin, E.M.1
  • 30
    • 84957167586 scopus 로고
    • English transl., Math. USSR-Sb. 37 (1980), 381-388.
    • (1980) Math. USSR-Sb. , vol.37 , pp. 381-388
  • 31
    • 85164646354 scopus 로고    scopus 로고
    • Diophantine approximations to Riemann's zeta function
    • (4 October, 2000), Mosk. Gos. Univ., Moscow
    • Yu. V. Nesterenko, "Diophantine approximations to Riemann's zeta function", Report on the Workshop on Number Theory (4 October, 2000), Mosk. Gos. Univ., Moscow 2000.
    • (2000) Report on the Workshop on Number Theory
    • Nesterenko, Yu.V.1
  • 32
    • 0003911106 scopus 로고
    • Grundlehren Math. Wiss, Springer-Verlag, Berlin ; Russian transl., Mir, Moscow
    • S. Lang, Introduction to modular forms, Grundlehren Math. Wiss., vol. 222, Springer-Verlag, Berlin 1976; Russian transl., Mir, Moscow 1979.
    • (1976) Introduction to Modular Forms , vol.222
    • Lang, S.1
  • 33
    • 0003930163 scopus 로고
    • North-Holland, Amsterdam ; Russian transl., Inostr. Lit., Moscow
    • N. G. de Bruijn, Asymptotic methods in analysis, North-Holland, Amsterdam 1958; Russian transl., Inostr. Lit., Moscow 1961.
    • (1958) Asymptotic Methods in Analysis
    • De Bruijn, N.G.1
  • 35
    • 0001669878 scopus 로고
    • On the method of Thue-Siegel
    • G. V. Chudnovsky, "On the method of Thue-Siegel", Ann. of Math. (2) 117 (1983), 325-382.
    • (1983) Ann. of Math. , vol.117 , Issue.2 , pp. 325-382
    • Chudnovsky, G.V.1
  • 36
    • 84961495106 scopus 로고
    • Legendre type polynomials and irrationality measures
    • M. Hata, "Legendre type polynomials and irrationality measures", J. Reine Angew. Math. 407:1 (1990), 99-125.
    • (1990) J. Reine Angew. Math. , vol.407 , Issue.1 , pp. 99-125
    • Hata, M.1
  • 38
    • 0042753428 scopus 로고    scopus 로고
    • One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational
    • V. V. Zudilin, "One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational", Uspekhi Mat. Nauk 56:4 (2001), 149-150;
    • (2001) Uspekhi Mat. Nauk , vol.56 , Issue.4 , pp. 149-150
    • Zudilin, V.V.1
  • 39
    • 0035634856 scopus 로고    scopus 로고
    • English transl.
    • English transl., Russian Math. Surveys 56 (2001), 774-776.
    • (2001) Russian Math. Surveys , vol.56 , pp. 774-776


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.