메뉴 건너뛰기




Volumn 8, Issue 3, 2002, Pages 475-521

Continued fractions, modular symbols, and noncommutative geometry

Author keywords

Dirichlet series; Gauss Kuzmin operator; K theory of C* algebras; Limiting modular symbols; Noncommutative modular curves

Indexed keywords


EID: 0013070377     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/s00029-002-8113-3     Document Type: Article
Times cited : (55)

References (45)
  • 1
    • 33646893145 scopus 로고
    • The entropy of a certain infinitely convolved Bernoulli measure
    • J. C. Alexander and D. Zagier. The entropy of a certain infinitely convolved Bernoulli measure. J. Land. Math. Soc. (2) 44 (1991), 121-134.
    • (1991) J. Land. Math. Soc. (2) , vol.44 , pp. 121-134
    • Alexander, J.C.1    Zagier, D.2
  • 3
    • 0003136519 scopus 로고
    • On a problem of Gauss
    • K. I. Babenko. On a problem of Gauss. Dokl. Akad. Nauk SSSR 238 (1978), no. 5, 1021-1024;
    • (1978) Dokl. Akad. Nauk SSSR , vol.238 , Issue.5 , pp. 1021-1024
    • Babenko, K.I.1
  • 4
    • 0001582715 scopus 로고
    • English translation. Soviet Math. Dokl. 19 (1978), no. 1, 136-140.
    • (1978) Soviet Math. Dokl. , vol.19 , Issue.1 , pp. 136-140
  • 5
    • 52649094874 scopus 로고
    • On a problem of Gauss
    • K. I. Babenko and S. P. Yurev. On a problem of Gauss. Sci. Math. Sov. Vol. 2 (1982), no. 4, 331-378.
    • (1982) Sci. Math. Sov. , vol.2 , Issue.4 , pp. 331-378
    • Babenko, K.I.1    Yurev, S.P.2
  • 6
    • 0005107336 scopus 로고
    • Chaotic behaviour and the Einstein equations
    • (W. Bonnor et al, eds.). Cambridge Univ. Press, Cambridge
    • J. D. Barrow. Chaotic behaviour and the Einstein equations. In: Classical General Relativity (W. Bonnor et al, eds.). Cambridge Univ. Press, Cambridge, 1984 25-41.
    • (1984) Classical General Relativity , pp. 25-41
    • Barrow, J.D.1
  • 7
    • 0014808945 scopus 로고
    • Oscillatory approach to singular point in Relativistic cosmology
    • V. Belinskii, I. M. Khalatnikov and E. M. Lifshitz. Oscillatory approach to singular point in Relativistic cosmology. Adv. Phys. 19 (1970), 525-551.
    • (1970) Adv. Phys. , vol.19 , pp. 525-551
    • Belinskii, V.1    Khalatnikov, I.M.2    Lifshitz, E.M.3
  • 9
    • 0010136756 scopus 로고
    • Singularities of cosmological model of Bianchi IX-type according to qualitative theory of differential equations
    • O. N. Bogoyavlenskii and S. P. Novikov. Singularities of cosmological model of Bianchi IX-type according to qualitative theory of differential equations. Sov. Phys. JETP 64 (1973), no. 5, 1475-1491.
    • (1973) Sov. Phys. JETP , vol.64 , Issue.5 , pp. 1475-1491
    • Bogoyavlenskii, O.N.1    Novikov, S.P.2
  • 11
    • 4043153496 scopus 로고
    • Cyclic cohomology of étale groupoids
    • J. L. Brylinski and V. Nistor. Cyclic cohomology of étale groupoids. K-theory 8 (1994), no. 4, 341-365.
    • (1994) K-theory , vol.8 , Issue.4 , pp. 341-365
    • Brylinski, J.L.1    Nistor, V.2
  • 12
    • 0001373445 scopus 로고    scopus 로고
    • Thermodynamic formalism and Selberg's zeta function for modular groups
    • C.-H. Chang and D. Mayer. Thermodynamic formalism and Selberg's zeta function for modular groups. Regular and Chaotic Dynamics 15 (2000), no. 3, 281-312.
    • (2000) Regular and Chaotic Dynamics , vol.15 , Issue.3 , pp. 281-312
    • Chang, C.-H.1    Mayer, D.2
  • 14
    • 0041524804 scopus 로고    scopus 로고
    • Non-commutative geometry and Matrix theory: Compactification on tori
    • Paper 3, (electronic)
    • A. Connes, M. Douglas and A. Schwarz. Non-commutative geometry and Matrix theory: compactification on tori. J. High Energy Phys. (1998), no. 2, Paper 3, 35 pp. (electronic).
    • (1998) J. High Energy Phys. , vol.2
    • Connes, A.1    Douglas, M.2    Schwarz, A.3
  • 15
    • 0000684032 scopus 로고    scopus 로고
    • The K-theory of Cuntz-Krieger algebras for infinite matrices
    • R. Exel and M. Laca,. The K-theory of Cuntz-Krieger algebras for infinite matrices. K-theory 19 (2000), no. 3, 251-268.
    • (2000) K-theory , vol.19 , Issue.3 , pp. 251-268
    • Exel, R.1    Laca, M.2
  • 16
    • 0042452279 scopus 로고    scopus 로고
    • Zeta functions formed with modular symbols
    • D. Goldfeld. Zeta functions formed with modular symbols. In: Proc. Symp. Pure Math. Vol. 66, (1999), no. 1, 111-121.
    • (1999) Proc. Symp. Pure Math. , vol.66 , Issue.1 , pp. 111-121
    • Goldfeld, D.1
  • 17
    • 0001250011 scopus 로고    scopus 로고
    • The distribution of modular symbols
    • (A. Schinzel's Festschrift), Walter de Gruyter, Berlin-New York
    • D. Goldfeld. The distribution of modular symbols. In: Number Theory in Progress (A. Schinzel's Festschrift), Walter de Gruyter, Berlin-New York, Vol. 2 (1999), 849-865.
    • (1999) Number Theory in Progress , vol.2 , pp. 849-865
    • Goldfeld, D.1
  • 18
    • 0031283601 scopus 로고    scopus 로고
    • The double logarithm and Manin's complex for modular curves
    • A. Goncharov. The double logarithm and Manin's complex for modular curves. Math. Res. Letters 4 (1997), 617-636.
    • (1997) Math. Res. Letters , vol.4 , pp. 617-636
    • Goncharov, A.1
  • 21
    • 0041082196 scopus 로고    scopus 로고
    • Purely infinite C*-algebras from boundary actions of dis-crete groups
    • M. Laca and J. Spielberg. Purely infinite C*-algebras from boundary actions of dis-crete groups. J. reine angew. Math. 480 (1996), 125-139.
    • (1996) J. Reine Angew. Math. , vol.480 , pp. 125-139
    • Laca, M.1    Spielberg, J.2
  • 22
    • 0012848870 scopus 로고    scopus 로고
    • Modular forms and quantum invariants of 3-manifolds
    • Atiyah's Festschrift
    • R. Lawrence and D. Zagier. Modular forms and quantum invariants of 3-manifolds. In: Asian J. Math. 3 (1999) (Atiyah's Festschrift), no. 1, 93-107.
    • (1999) Asian J. Math. , vol.3 , Issue.1 , pp. 93-107
    • Lawrence, R.1    Zagier, D.2
  • 23
    • 0000172957 scopus 로고
    • Sur les lois de probabilité dont dépendent les quotients complets et incomplets d'une fraction continue
    • P. Levy. Sur les lois de probabilité dont dépendent les quotients complets et incomplets d'une fraction continue. Bull. Soc. Math. France 557 (1929), 178-194.
    • (1929) Bull. Soc. Math. France , vol.557 , pp. 178-194
    • Levy, P.1
  • 24
    • 0039613553 scopus 로고    scopus 로고
    • Period functions and the Seiberg zeta function for the modular group
    • The Mathematical Beauty of Physics, World Scientific, Singapore
    • J. Lewis and D. Zagier. Period functions and the Seiberg zeta function for the modular group. In: The Mathematical Beauty of Physics, Adv. Series in Math. Physics 24, World Scientific, Singapore, 1997, pp. 83-9.
    • (1997) Adv. Series in Math. Physics , vol.24 , pp. 83-89
    • Lewis, J.1    Zagier, D.2
  • 26
    • 0002672437 scopus 로고
    • Parabolic points and zeta-functions of modular curves
    • Yu. Manin. Parabolic points and zeta-functions of modular curves. Math. USSR Izvestija 6 (1972), no. 1, 19-64;
    • (1972) Math. USSR Izvestija , vol.6 , Issue.1 , pp. 19-64
    • Manin, Y.1
  • 27
    • 52649153021 scopus 로고    scopus 로고
    • World Scientific
    • and Selected Papers, World Scientific, 1996, 202-247.
    • (1996) Selected Papers , pp. 202-247
  • 28
    • 3543002625 scopus 로고
    • Explicit formulas for the eigenvalues of Hecke operators
    • Yu. Manin. Explicit formulas for the eigenvalues of Hecke operators. Acta Arithmetica 24 (1973), 239-249.
    • (1973) Acta Arithmetica , vol.24 , pp. 239-249
    • Manin, Y.1
  • 29
    • 0000079563 scopus 로고
    • Three-dimensional hyperbolic geometry as ∞-adic Arakelov geometry
    • Yu. Manin. Three-dimensional hyperbolic geometry as ∞-adic Arakelov geometry. Inv. Math. 104 (1991), 223-244.
    • (1991) Inv. Math. , vol.104 , pp. 223-244
    • Manin, Y.1
  • 30
    • 0042582072 scopus 로고    scopus 로고
    • Mirror symmetry and quantization of abelian varieties
    • Texel Island, Prog. Math. Birkhäuser, Basel, 2001
    • Yu. Manin. Mirror symmetry and quantization of abelian varieties. In: Moduli of abelian varieties (Texel Island, 1999) 231-254, Prog. Math. Birkhäuser, Basel, 2001.
    • (1999) Moduli of Abelian Varieties , pp. 231-254
    • Manin, Y.1
  • 31
    • 84956098188 scopus 로고
    • Periods of parabolic forms and p-adic Hecke series
    • Yu. Manin. Periods of parabolic forms and p-adic Hecke series. Math. USSR Sbornik 21 (1973), no. 3, 371-393;
    • (1973) Math. USSR Sbornik , vol.21 , Issue.3 , pp. 371-393
    • Manin, Y.1
  • 32
    • 52649153021 scopus 로고    scopus 로고
    • World Scientific
    • and Selected Papers, World Scientific, 1996, 268-297.
    • (1996) Selected Papers , pp. 268-297
  • 34
    • 0002562682 scopus 로고
    • Continued fractions and related transformations
    • (T. Bedford et al., eds.). Oxford University Press, Oxford
    • D. Mayer. Continued fractions and related transformations. In: Ergodic Theory, Sym-bolic Dynamics and Hyperbolic Spaces (T. Bedford et al., eds.). Oxford University Press, Oxford, 1991 175-222.
    • (1991) Ergodic Theory, Sym-bolic Dynamics and Hyperbolic Spaces , pp. 175-222
    • Mayer, D.1
  • 35
    • 0040780449 scopus 로고
    • Relaxation properties of the Mixmaster Universe
    • D. H. Mayer. Relaxation properties of the Mixmaster Universe. Phys. Lett. A 121 (1987), no. 8,9, 390-394.
    • (1987) Phys. Lett. A , vol.121 , Issue.8-9 , pp. 390-394
    • Mayer, D.H.1
  • 36
    • 0013158553 scopus 로고
    • Intersections sur les courbes modulaires
    • L. Merel. Intersections sur les courbes modulaires. Manuscripta Math. 80 (1993), 283-289.
    • (1993) Manuscripta Math. , vol.80 , pp. 283-289
    • Merel, L.1
  • 37
    • 0000041234 scopus 로고
    • Group cohomology and cyclic cohomology of crossed products
    • V. Nistor. Group cohomology and cyclic cohomology of crossed products. Invent. Math. 99 (1990), 411-424.
    • (1990) Invent. Math. , vol.99 , pp. 411-424
    • Nistor, V.1
  • 38
    • 0034344446 scopus 로고    scopus 로고
    • Properties of Eisenstein series formed with modular symbols
    • C. O'Sullivan. Properties of Eisenstein series formed with modular symbols. J. reine u. angew. Math. 518 (2000), 163-186.
    • (2000) J. Reine U. Angew. Math. , vol.518 , pp. 163-186
    • O'Sullivan, C.1
  • 39
    • 0000940119 scopus 로고
    • KK-groups of crossed products by groups acting on trees
    • M. Pimsner. KK-groups of crossed products by groups acting on trees. Invent. Math. 86 (1986), 603-634.
    • (1986) Invent. Math. , vol.86 , pp. 603-634
    • Pimsner, M.1
  • 42
    • 0038182402 scopus 로고    scopus 로고
    • Quantum tori, mirror symetry and deformation theory
    • Y. Soibelman. Quantum tori, mirror symetry and deformation theory. Lett. Math. Phys. 56 (2001), no. 2, 99-125.
    • (2001) Lett. Math. Phys. , vol.56 , Issue.2 , pp. 99-125
    • Soibelman, Y.1
  • 43
    • 0344429692 scopus 로고
    • Cuntz-Krieger algebras associated with Fuchsian groups
    • J. S. Spielberg. Cuntz-Krieger algebras associated with Fuchsian groups. Ergod. Th. Dynam. Sys. 13 (1993), 581-595.
    • (1993) Ergod. Th. Dynam. Sys. , vol.13 , pp. 581-595
    • Spielberg, J.S.1
  • 44
    • 34250398203 scopus 로고
    • Remarks on invariant measures for number theoretic transformations
    • M. S. Waterman. Remarks on invariant measures for number theoretic transformations. Monatshefte für Mathematik 79 (1975), 157-163.
    • (1975) Monatshefte für Mathematik , vol.79 , pp. 157-163
    • Waterman, M.S.1
  • 45
    • 0001195414 scopus 로고    scopus 로고
    • Vassiliev invariants and a strange identity related to the Dedekind etafunction
    • D. Zagier. Vassiliev invariants and a strange identity related to the Dedekind etafunction. Topology 40 (2001), no. 5, 945-960.
    • (2001) Topology , vol.40 , Issue.5 , pp. 945-960
    • Zagier, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.