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AN ALGEBRO-GEOMETRIC STUDY OF SPECIAL VALUES OF HYPERGEOMETRIC FUNCTIONS $_{3}F_{2}$

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

Published online by Cambridge University Press:  13 September 2018

MASANORI ASAKURA ,
NORIYUKI OTSUBO  and
TOMOHIDE TERASOMA
MASANORI ASAKURA
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan email [email protected]
NORIYUKI OTSUBO
Affiliation:
Department of Mathematics and Informatics, Chiba University, Chiba, 263-8522, Japan email [email protected]
TOMOHIDE TERASOMA
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, 153-8914, Japan email [email protected]
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Abstract

For a certain class of hypergeometric functions $_{3}F_{2}$ with rational parameters, we give a sufficient condition for the special value at $1$ to be expressed in terms of logarithms of algebraic numbers. We give two proofs, both of which are algebro-geometric and related to higher regulators.

MSC classification

Primary: 14D07: Variation of Hodge structures 19F27: Étale cohomology, higher regulators, zeta and $L$-functions 33C20: Generalized hypergeometric series, $_pF_q$
Secondary: 11G15: Complex multiplication and moduli of abelian varieties 14K22: Complex multiplication
Type
Article
Information
Nagoya Mathematical Journal , Volume 236: Celebrating the 60th Birthday of Shuji Saito , December 2019 , pp. 47 - 62
Copyright
© 2018 Foundation Nagoya Mathematical Journal  

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Footnotes

This work is supported by JSPS Grant-in-Aid for Scientific Research: 15K04769, 25400007 and 15H02048.

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