Euler and Laplace integral representations of GKZ hypergeometric functions
Classical Analysis and ODEs
2020-12-29 v4 Algebraic Geometry
Analysis of PDEs
Abstract
We introduce an interpolation between Euler integral and Laplace integral: Euler-Laplace integral. We establish a combinatorial method of constructing a basis of the rapid decay homology group associated to Euler-Laplace integral with a nice intersection property. This construction yields a remarkable expansion formula of cohomology intersection numbers in terms of GKZ hypergeometric series. As an application, we obtain closed formulas of the quadratic relations of Aomoto-Gelfand hypergeometric functions and their confluent analogue in terms of bipartite graphs.
Cite
@article{arxiv.1904.00565,
title = {Euler and Laplace integral representations of GKZ hypergeometric functions},
author = {Saiei-Jaeyeong Matsubara-Heo},
journal= {arXiv preprint arXiv:1904.00565},
year = {2020}
}
Comments
61 pages, 18 figures. Any comment is welcome