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The monodromy representation and twisted period relations for Appell’s hypergeometric function F4

Published online by Cambridge University Press:  11 January 2016

Yoshiaki Goto
Affiliation:
Department of Mathematics, Graduate School of Science, Kobe University, Kobe 657-8501, Japan, [email protected]
Keiji Matsumoto
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan, [email protected]
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Abstract

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We consider the system F4 (a, b, c) of differential equations annihilating Appell's hypergeometric series F4(a,b,c;x). We find the integral representations for four linearly independent solutions expressed by the hypergeometric series F4. By using the intersection forms of twisted (co)homology groups associated with them, we provide the monodromy representation of F4(a, b, c) and the twisted period relations for the fundamental systems of solutions of F4.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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