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A FUNCTIONAL LOGARITHMIC FORMULA FOR THE HYPERGEOMETRIC FUNCTION $_{3}F_{2}$

Part of: $K$-theory in number theory Arithmetic algebraic geometry Abelian varieties and schemes Families, fibrations

Published online by Cambridge University Press:  14 September 2018

MASANORI ASAKURA  and
NORIYUKI OTSUBO
MASANORI ASAKURA
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, 060-0810 Japan email asakura@math.sci.hokudai.ac.jp
NORIYUKI OTSUBO
Affiliation:
Department of Mathematics and Informatics, Chiba University, Chiba, 263-8522 Japan email otsubo@math.s.chiba-u.ac.jp
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Abstract

We give a sufficient condition for the hypergeometric function $_{3}F_{2}$ to be a linear combination of the logarithm of algebraic functions.

MSC classification

Primary: 33C20: Generalized hypergeometric series, $_pF_q$
Secondary: 19F27: Étale cohomology, higher regulators, zeta and $L$-functions 11G15: Complex multiplication and moduli of abelian varieties 14D07: Variation of Hodge structures 14K22: Complex multiplication
Type
Article
Information
Nagoya Mathematical Journal , Volume 236: Celebrating the 60th Birthday of Shuji Saito , December 2019 , pp. 29 - 46
Copyright
© 2018 Foundation Nagoya Mathematical Journal  

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References

Archinard, N., Hypergeometric abelian varieties , Canad. J. Math. 55 (2003), 897–932.10.4153/CJM-2003-037-4Google Scholar
Asakura, M. and Fresán, J., On the Gross–Deligne conjecture for variations of Hodge–de Rham structures, preprint.Google Scholar
Asakura, M. and Otsubo, N., Regulators on $K_{1}$ of hypergeometric fibrations, to appear in the Proceedings of Conference “Arithmetic $L$ -functions and Differential Geometric Methods (Regulators IV)”, arXiv:1709.04144.Google Scholar
Asakura, M. and Otsubo, N., CM periods, CM regulators and hypergeometric functions, II , Math. Z. 289(3–4) (2018), 1325–1355.10.1007/s00209-017-2001-1Google Scholar
Asakura, M., Otsubo, N. and Terasoma, T., An algebro-geometric study of special values of hypergeometric functions 3 F 2 , Nagoya Math. J. 236 (2019), 47–62.Google Scholar
Bailey, W. N., Generalized hypergeometric series, Cambridge Tracts in Mathematics and Mathematical Physics 32 , Stechert-Hafner, Inc., New York, 1964.Google Scholar
Beukers, F. and Heckman, G., Monodromy for the hypergeometric function n F n-1 , Invent. Math. 95(2) (1989), 325–354.10.1007/BF01393900Google Scholar
Erdélyi, A. (eds), Higher transcendental functions, Vol. 1, McGrow-Hill, New York, 1953.Google Scholar
Fedorov, R., Variations of Hodge structures for hypergeometric differential operators and parabolic Higgs bundles, arXiv:1505.01704.Google Scholar
Olver, F. W. J., Lozier, D. W., Boisvert, R. F. and Clark, C. W. (eds), NIST handbook of mathematical functions, Cambridge University Press, Cambridge, 2010.Google Scholar
Slater, L. J., Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966.Google Scholar
Steenbrink, J., Limits of Hodge structures , Invent. Math. 31(3) (1976), 229–257.10.1007/BF01403146Google Scholar