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November 2020 Euler and Laplace integral representations of GKZ hypergeometric functions I
Saiei-Jaeyeong Matsubara-Heo
Proc. Japan Acad. Ser. A Math. Sci. 96(9): 75-78 (November 2020). DOI: 10.3792/pjaa.96.014

Abstract

We introduce an interpolation between Euler integral and Laplace integral: Euler-Laplace integral. We claim that, when parameters $\delta$ of the integrand are non-resonant, the $\mathcal{D}$-module corresponding to Euler-Laplace integral is naturally isomorphic to GKZ hypergeometric system $M_{A}(\delta)$ where $A$ is a generalization of Cayley configuration. As a topological counterpart of this isomorphism, we establish an isomorphism between certain rapid decay homology group and holomorphic solutions of $M_{A}(\delta)$.

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Saiei-Jaeyeong Matsubara-Heo. "Euler and Laplace integral representations of GKZ hypergeometric functions I." Proc. Japan Acad. Ser. A Math. Sci. 96 (9) 75 - 78, November 2020. https://doi.org/10.3792/pjaa.96.014

Information

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

MathSciNet: MR4170181
Digital Object Identifier: 10.3792/pjaa.96.014

Subjects:
Primary: 33D70
Secondary: 32C38

Rights: Copyright © 2020 The Japan Academy

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Vol.96 • No. 9 • November 2020
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