Hyperlogarithmic expansion and the volume of a hyperbolic simplex

K. Aomoto

Banach Center Publications (1992)

  • Volume: 27, Issue: 1, page 9-21
  • ISSN: 0137-6934

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Aomoto, K.. "Hyperlogarithmic expansion and the volume of a hyperbolic simplex." Banach Center Publications 27.1 (1992): 9-21. <http://eudml.org/doc/262870>.

@article{Aomoto1992,
author = {Aomoto, K.},
journal = {Banach Center Publications},
keywords = {simplex volume; regularization; technique; hyperlogarithmic functions},
language = {eng},
number = {1},
pages = {9-21},
title = {Hyperlogarithmic expansion and the volume of a hyperbolic simplex},
url = {http://eudml.org/doc/262870},
volume = {27},
year = {1992},
}

TY - JOUR
AU - Aomoto, K.
TI - Hyperlogarithmic expansion and the volume of a hyperbolic simplex
JO - Banach Center Publications
PY - 1992
VL - 27
IS - 1
SP - 9
EP - 21
LA - eng
KW - simplex volume; regularization; technique; hyperlogarithmic functions
UR - http://eudml.org/doc/262870
ER -

References

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  1. [A1] K. Aomoto, Fonctions hyper-logarithmiques et groupes de monodromie unipotents, J. Fac. Sci. Univ. Tokyo 25 (1973), 149-156. Zbl0416.32020
  2. [A2] K. Aomoto, On structure of integrals of power product linear functions, Sci. Papers Col. Gen. Edu. Univ. Tokyo 27 (1977), 49-61. 
  3. [A3] K. Aomoto, Configurations and invariant Gauss-Manin connections of integrals I, Tokyo J. Math. 5 (1982), 249-287; II, ibid. 6 (1983), 1-24. Zbl0524.32005
  4. [A4] K. Aomoto, Vanishing of certain 1-form attached to a configuration, ibid. 9 (1986), 453-455. 
  5. [A5] K. Aomoto, Analytic structure of Schläfli function, Nagoya Math. J. 68 (1977), 1-16. Zbl0382.33010
  6. [B1] A. A. Beilinson, A. Varchenko and V. Schechtman, Projective geometry and K-theory, Algebra and Anal. 2 (1990), 78-130. 
  7. [B2] J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeometric functions, Quart. J. Math. 11 (1940), 249-270. Zbl0025.16301
  8. [G1] I. M. Gelfand and A. V. Zelevinski, Algebraic and combinatorial aspect of general theory of hypergeometric functions, Funct. Anal. Appl. 20 (1986), 17-34. 
  9. [G2] A. B. Goncharov, The classical trilogarithm, algebraic K-theory of fields and Dedekind zeta functions, preprint, 1990. 
  10. [H1] R. Hain, The geometry of the mixed Hodge structure on the fundamental group, in: Proc. Sympos. Pure Math. 46, Amer. Math. Soc., 1987, 247-282. 
  11. [H2] R. Hain and R. MacPherson, Higher logarithms, Illinois J. Math. 34 (1990), 392-475. Zbl0737.14014
  12. [K1] J. Kaneko, Monodromy group of Appell’s system ( F 4 ) , Tokyo J. Math. 4 (1981), 35-54. Zbl0474.33010
  13. [K2] J. Kaneko, Selberg integrals and hypergeometric functions, preprint, 1990. 
  14. [K3] M. Kashiwara and P. Schapira, Sheaves on Manifolds, Chap. XI, Springer, 1990. 
  15. [K4] R. Kellerhals, On the volume of hyperbolic polyhedra, Math. Ann. 285 (1989), 541-569. Zbl0664.51012
  16. [K5] R. Kellerhals, The dilogarithm and volumes of hyperbolic polytopes, preprint. 
  17. [M1] J. Milnor, Hyperbolic geometry. The first 150 years, Bull. Amer. Math. Soc. 6 (1982), 9-24. Zbl0486.01006
  18. [M2] J. Milnor, On polylogarithms, Hurwitz zeta functions, and the Kubert identities, Enseign. Math. 29 (1983), 281-322. Zbl0557.10031
  19. [V] A. Varchenko, Multidimensional hypergeometric functions and their appearance in conformal field theory. Algebraic K-theory, algebraic geometry, etc., congress talk in Kyoto, 1990. 
  20. [W] Z. Wojtkowiak, A note on functional equations of polylogarithms, preprint, 1990. 
  21. [Z] D. Zagier, Hyperbolic manifolds and special values of Dedekind zeta functions, Invent. Math. 83 (1986), 285-301. Zbl0591.12014

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