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November 2020 Euler and Laplace integral representations of GKZ hypergeometric functions II
Saiei-Jaeyeong Matsubara-Heo
Proc. Japan Acad. Ser. A Math. Sci. 96(9): 79-82 (November 2020). DOI: 10.3792/pjaa.96.015

Abstract

We establish the intersection theory of the rapid decay homology group and formulate the twisted period relation in this setting. We claim that there is a standard method of constructing a basis of the rapid decay homology group which can be related to GKZ hypergeometric series. This can be carried out with the aid of a convergent regular triangulation $T$. When $T$ is unimodular, we can obtain a closed formula of the homology intersection number. Finally, we obtain a Laurent series expansion formula of the cohomology intersection number in terms of the combinatorics of $T$.

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Saiei-Jaeyeong Matsubara-Heo. "Euler and Laplace integral representations of GKZ hypergeometric functions II." Proc. Japan Acad. Ser. A Math. Sci. 96 (9) 79 - 82, November 2020. https://doi.org/10.3792/pjaa.96.015

Information

Published: November 2020
First available in Project Euclid: 4 November 2020

MathSciNet: MR4170182
Digital Object Identifier: 10.3792/pjaa.96.015

Subjects:
Primary: 12F12
Secondary: 12F13

Rights: Copyright © 2020 The Japan Academy

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Vol.96 • No. 9 • November 2020
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