메뉴 건너뛰기




Volumn , Issue , 2007, Pages 3-65

The dilogarithm function

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84895298106     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-30308-4_1     Document Type: Chapter
Times cited : (347)

References (59)
  • 1
    • 0038747743 scopus 로고
    • Applications of the dilogarithm function in algebraic K-theory and algebraic geometry
    • Kinokuniya, Tokyo
    • S. BLOCH: Applications of the dilogarithm function in algebraic K-theory and algebraic geometry, in: Proc. of the International Symp. on Alg. Geometry, Kinokuniya, Tokyo, 1978.
    • (1978) Proc. of the International Symp. on Alg. Geometry
    • Bloch, S.1
  • 2
    • 0002045519 scopus 로고
    • Commensurability classes and volumes of hyperbolic 3-manifolds
    • A. BOREL: Commensurability classes and volumes of hyperbolic 3-manifolds, Ann. Sc. Norm. Sup. Pisa, 8 (1981), 1-33.
    • (1981) Ann. Sc. Norm. Sup. Pisa , vol.8 , pp. 1-33
    • Borel, A.1
  • 5
    • 0000459324 scopus 로고
    • Volumes of hyperbolic 3-manifolds
    • W. NEUMANN and D. ZAGIER: Volumes of hyperbolic 3-manifolds, Topology, 24 (1985), 307-332.
    • (1985) Topology , vol.24 , pp. 307-332
    • Neumann, W.1    Zagier, D.2
  • 6
    • 0007026649 scopus 로고
    • Analogs of the Bloch-Wigner function for higher polylogarithms
    • D. RAMAKRISHNAN: Analogs of the Bloch-Wigner function for higher polylogarithms, Contemp. Math., 55 (1986), 371-376.
    • (1986) Contemp. Math. , vol.55 , pp. 371-376
    • Ramakrishnan, D.1
  • 8
    • 0009987847 scopus 로고
    • Hyperbolic manifolds and special values of Dedekind zeta-functions
    • D. ZAGIER: Hyperbolic manifolds and special values of Dedekind zeta-functions, Invent. Math., 83 (1986), 285-301.
    • (1986) Invent. Math. , vol.83 , pp. 285-301
    • Zagier, D.1
  • 11
  • 14
    • 0141457257 scopus 로고    scopus 로고
    • Finite and p-adic polylogarithms
    • Besser, A.: Finite and p-adic polylogarithms. Compositio Math. 130 (2002) 215-223.
    • (2002) Compositio Math. , vol.130 , pp. 215-223
    • Besser, A.1
  • 15
    • 0000425674 scopus 로고
    • n et valeurs de fonctions ẑeta aux points entiers
    • n et valeurs de fonctions ẑeta aux points entiers. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4 (1977) 613-636.
    • (1977) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.4 , pp. 613-636
    • Borel, A.1
  • 17
    • 0034393903 scopus 로고    scopus 로고
    • Computing the tame kernel of quadratic imaginary fields. with an appendix by Karim Belabas and Herbert Gangl
    • Browkin, J.: Computing the tame kernel of quadratic imaginary fields. With an appendix by Karim Belabas and Herbert Gangl. Math. Comp. 69 (2000) 1667-1683.
    • (2000) Math. Comp. , vol.69 , pp. 1667-1683
    • Browkin, J.1
  • 18
    • 0038101778 scopus 로고    scopus 로고
    • Remarques sur les différentielles des polylogarithmes uniformes
    • Cathelineau, J.-L.: Remarques sur les différentielles des polylogarithmes uniformes. Ann. Inst. Fourier Grenoble 46 (1996), 1327-1347.
    • (1996) Ann. Inst. Fourier Grenoble , vol.46 , pp. 1327-1347
    • Cathelineau, J.-L.1
  • 20
    • 0039856348 scopus 로고
    • A sixteenth-order polylogarithm ladder
    • Cohen, H., Lewin L. and Zagier, D.: A sixteenth-order polylogarithm ladder. Experimental Math. 1 (1992) 25-34.
    • (1992) Experimental Math. , vol.1 , pp. 25-34
    • Cohen, H.1    Lewin, L.2    Zagier, D.3
  • 21
    • 0000697453 scopus 로고
    • Dilogarithms, regulators and p-adic L-functions
    • Coleman, R.: Dilogarithms, regulators and p-adic L-functions. Invent. Math. 69 (1982), 171-208.
    • (1982) Invent. Math. , vol.69 , pp. 171-208
    • Coleman, R.1
  • 22
    • 0039762390 scopus 로고
    • Zagier's conjecture and wedge complexes in algebraic K-theory
    • de Jeu, R.: Zagier's conjecture and wedge complexes in algebraic K-theory. Compositio Math. 96 (1995) 197-247.
    • (1995) Compositio Math. , vol.96 , pp. 197-247
    • De Jeu, R.1
  • 23
    • 0001871379 scopus 로고
    • Higher regulators and Hecke L-series of imaginary quadratic fields. i
    • Deninger, C.: Higher regulators and Hecke L-series of imaginary quadratic fields. I. Invent. Math. 96 (1989) 1-69.
    • (1989) Invent. Math. , vol.96 , pp. 1-69
    • Deninger, C.1
  • 26
    • 77956961089 scopus 로고    scopus 로고
    • Functional equations for higher logarithms
    • Gangl, H.: Functional equations for higher logarithms. Selecta Math. 9 (2003) 361-377.
    • (2003) Selecta Math. , vol.9 , pp. 361-377
    • Gangl, H.1
  • 27
    • 0002257741 scopus 로고
    • ADE functional dilogarithm identities and inte-grable models
    • Gliozzi, F.; Tateo, R.: ADE functional dilogarithm identities and inte-grable models. Phys. Lett. B 348 (1995) 84-88.
    • (1995) Phys. Lett. B , vol.348 , pp. 84-88
    • Gliozzi, F.1    Tateo, R.2
  • 28
    • 0000412896 scopus 로고    scopus 로고
    • Thermodynamic Bethe ansatz and three-fold triangulations
    • Gliozzi, F.; Tateo, R.: Thermodynamic Bethe ansatz and three-fold triangulations. Internat. J. Modern Phys. A 11 (1996) 4051-4064.
    • (1996) Internat. J. Modern Phys. A , vol.11 , pp. 4051-4064
    • Gliozzi, F.1    Tateo, R.2
  • 29
    • 0000320221 scopus 로고
    • Unitary representations of the Vi-rasoro and supervirasoro algebras
    • Goddard, P., Kent, A. and Olive, D.: Unitary representations of the Vi-rasoro and supervirasoro algebras. Commun. Math. Phys. 103 (1986) 105-119.
    • (1986) Commun. Math. Phys. , vol.103 , pp. 105-119
    • Goddard, P.1    Kent, A.2    Olive, D.3
  • 30
    • 0007021265 scopus 로고
    • Geometry of configurations, polylogarithms, and mo-tivic cohomology
    • Goncharov, A. B.: Geometry of configurations, polylogarithms, and mo-tivic cohomology. Adv. Math. 114 (1995) 197-318.
    • (1995) Adv. Math. , vol.114 , pp. 197-318
    • Goncharov, A.B.1
  • 31
    • 0031283601 scopus 로고    scopus 로고
    • The double logarithm and Manin's complex for modular curves
    • Goncharov, A. B.: The double logarithm and Manin's complex for modular curves. Math. Res. Lett. 4 (1997) 617-636.
    • (1997) Math. Res. Lett. , vol.4 , pp. 617-636
    • Goncharov, A.B.1
  • 32
    • 0002987278 scopus 로고
    • Dilogarithm identities. in Quantum field theory, integrable models and beyond, Kyoto 1994
    • Kirillov, A.N.: Dilogarithm identities. In Quantum field theory, integrable models and beyond, Kyoto 1994. Progress of Theoretical Physics Supplement 118 (1995) 61-142.
    • (1995) Progress of Theoretical Physics Supplement , vol.118 , pp. 61-142
    • Kirillov, A.N.1
  • 33
    • 0348062656 scopus 로고    scopus 로고
    • 2-logarithm
    • = Appendix to[14].)
    • 2-logarithm. Compositio Math. 130 (2002) 211-214. (= Appendix to[14].)
    • (2002) Compositio Math. , vol.130 , pp. 211-214
    • Kontsevich, M.1
  • 34
    • 0012848870 scopus 로고    scopus 로고
    • Modular forms and quantum invariants of 3-manifolds
    • Lawrence, R. and Zagier, D.: Modular forms and quantum invariants of 3-manifolds. Asian J. of Math. 3 (1999) 93-108.
    • (1999) Asian J. of Math. , vol.3 , pp. 93-108
    • Lawrence, R.1    Zagier, D.2
  • 35
    • 84895307639 scopus 로고    scopus 로고
    • Kronecker double series and the dilogarithm. in Number theory and algebraic geometry
    • Cambridge Univ. Press
    • Levin, A.: Kronecker double series and the dilogarithm. In Number theory and algebraic geometry, London Math. Soc. Lecture Note Ser. 303, Cambridge Univ. Press (2003) 177-201.
    • (2003) London Math. Soc. Lecture Note Ser. , vol.303 , pp. 177-201
    • Levin, A.1
  • 36
    • 33646872086 scopus 로고
    • Uber Partitionen mit Differenzenbedingungen
    • Meinardus G.: Uber Partitionen mit Differenzenbedingungen. Math. Z. 1 (1954) 289-302.
    • (1954) Math. Z. , vol.1 , pp. 289-302
    • Meinardus, G.1
  • 40
  • 41
    • 0001697657 scopus 로고
    • Dilogarithm identities in conformal field theory
    • Nahm, W., Recknagel, A. and Terhoeven, M. Dilogarithm identities in conformal field theory. Mod. Phys. Lett. A8 (1993) 1835-1847.
    • (1993) Mod. Phys. Lett. , vol.A8 , pp. 1835-1847
    • Nahm, W.1    Recknagel, A.2    Terhoeven, M.3
  • 42
    • 0000459324 scopus 로고
    • Volumes of hyperbolic three-manifolds
    • Neumann, W. and Zagier, D.: Volumes of hyperbolic three-manifolds. To po l og y 24 (1985) 307-332.
    • (1985) Topology , vol.24 , pp. 307-332
    • Neumann, W.1    Zagier, D.2
  • 43
    • 4243068575 scopus 로고    scopus 로고
    • Extended Bloch group and the Cheeger-Chern-Simons class
    • Neumann, W.: Extended Bloch group and the Cheeger-Chern-Simons class. Geom. Topol. 8 (2004) 413-474.
    • (2004) Geom. Topol. , vol.8 , pp. 413-474
    • Neumann, W.1
  • 44
    • 0040456990 scopus 로고    scopus 로고
    • On a permutation group related to ζ(2)
    • Rhin, G. and Viola, C.: On a permutation group related to ζ(2). Acta Arith. 77 (1996) 23-56.
    • (1996) Acta Arith. , vol.77 , pp. 23-56
    • Rhin, G.1    Viola, C.2
  • 45
    • 0000344728 scopus 로고
    • Polylogarithm identities in a conformal field theory in three-dimensions
    • Sachdev, S.: Polylogarithm identities in a conformal field theory in three-dimensions. Phys. Lett. B309 (1993) 285-288.
    • (1993) Phys. Lett. , vol.B309 , pp. 285-288
    • Sachdev, S.1
  • 46
    • 0001219663 scopus 로고
    • Dilogarithm identities, fusion rules and structure constants of CFTs
    • Terhoeven, M.: Dilogarithm identities, fusion rules and structure constants of CFTs. Mod. Phys. Lett. A9 (1994) 133-142.
    • (1994) Mod. Phys. Lett. , vol.A9 , pp. 133-142
    • Terhoeven, M.1
  • 48
    • 33749412616 scopus 로고
    • Yang-Baxterization of a quantum dilogarithm
    • J. Math. Sci. 88 (1998) 202-207
    • Volkov, A. Y. and Faddeev, L. D.: Yang-Baxterization of a quantum dilogarithm. Zap. Nauchn. Sem. S.-Peterburg 224 (1995) 146-154; J. Math. Sci. 88 (1998) 202-207.
    • (1995) Zap. Nauchn. Sem. S.-Peterburg , vol.224 , pp. 146-154
    • Volkov, A.Y.1    Faddeev, L.D.2
  • 49
    • 0033582403 scopus 로고    scopus 로고
    • Airy function-exact WKB results for potentials of odd degree
    • Voros, A.: Airy function-exact WKB results for potentials of odd degree. J. Phys. A 32 (1999) 1301-1311.
    • (1999) J. Phys. A , vol.32 , pp. 1301-1311
    • Voros, A.1
  • 50
    • 0039932194 scopus 로고    scopus 로고
    • Functional equations of iterated integrals with regular singularities
    • Wojtkowiak, Z.: Functional equations of iterated integrals with regular singularities. Nagoya Math. J. 142 (1996) 145-159.
    • (1996) Nagoya Math. J. , vol.142 , pp. 145-159
    • Wojtkowiak, Z.1
  • 51
    • 0141701631 scopus 로고
    • A note on functional equations of the p-adic polyloga-rithms
    • Wojtkowiak, Z.: A note on functional equations of the p-adic polyloga-rithms. Bull. Soc. Math. France 119 (1991), 343-370.
    • (1991) Bull. Soc. Math. France , vol.119 , pp. 343-370
    • Wojtkowiak, Z.1
  • 52
    • 44949284976 scopus 로고
    • On ideal points of deformation curves of hyperbolic 3-manifolds with one cusp
    • Yoshida, T.: On ideal points of deformation curves of hyperbolic 3-manifolds with one cusp. To po l og y 30 (1991) 155-170.
    • (1991) To Po L Og y , vol.30 , pp. 155-170
    • Yoshida, T.1
  • 53
    • 0038575431 scopus 로고    scopus 로고
    • The remarkable dilogarithm
    • also appeared as: "The dilogarithm function in geometry and number theory" in Number Theory and Related Topics, papers presented at the Ramanujan Colloquium, Bombay 1988, Tata and Oxford 231-249
    • Zagier, D.: The remarkable dilogarithm. J. Math. and Phys. Sciences 22 131-145; also appeared as: "The dilogarithm function in geometry and number theory" in Number Theory and Related Topics, papers presented at the Ramanujan Colloquium, Bombay 1988, Tata and Oxford 231-249.
    • J. Math. and Phys. Sciences , vol.22 , pp. 131-145
    • Zagier, D.1
  • 54
    • 0000830962 scopus 로고
    • The Bloch-Wigner-Ramakrishnan polylogarithm function
    • Zagier, D.: The Bloch-Wigner-Ramakrishnan polylogarithm function. Math. Annalen 286 (1990) 613-624.
    • (1990) Math. Annalen , vol.286 , pp. 613-624
    • Zagier, D.1
  • 55
    • 0007080088 scopus 로고
    • Polylogarithms, Dedekind zeta functions, and the algebraic K-theory of fields
    • (G. v.d. Geer, F. Oort, J. Steenbrink, eds.), Prog. in Math. Birkḧauser, Boston
    • Zagier, D.: Polylogarithms, Dedekind zeta functions, and the algebraic K-theory of fields. In Arithmetic Algebraic Geometry (G. v.d. Geer, F. Oort, J. Steenbrink, eds.), Prog. in Math. 89, Birkḧauser, Boston (1990) 391-430.
    • (1990) Arithmetic Algebraic Geometry , vol.89 , pp. 391-430
    • Zagier, D.1
  • 56
    • 0010154869 scopus 로고
    • Special values and functional equations of polylogarithms
    • ed. L. Lewin, Mathematical Surveys and Monographs 37, AMS, Providence
    • Zagier, D.: Special values and functional equations of polylogarithms. In The Structural Properties of Polylogarithms, ed. L. Lewin, Mathematical Surveys and Monographs 37, AMS, Providence (1991) 377-400.
    • (1991) The Structural Properties of Polylogarithms , pp. 377-400
    • Zagier, D.1
  • 58
    • 84895328937 scopus 로고    scopus 로고
    • Preprint, Bonn and Moscow
    • Zudilin, W.: Quantum dilogarithm. Preprint, Bonn and Moscow (2006), 8 pages.
    • (2006) Quantum Dilogarithm , pp. 8
    • Zudilin, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.