Appell-Lauricella's hypergeometric functions and intersection theory
February 15, 2022
We study hypergeometric functions by applying the intersection theory for twisted homology and cohomology groups, which arise from their Euler-type integral representations.
In this article, we consider Appell-Lauricella's hypergeometric functions which are
classical generalizations of Gauss' hypergeometric function. Especially, we focus on Lauricella's $F_A$ and $F_C$, and study them by using intersection theory. By evaluating some intersection numbers, we obtain quadratic relations between $F_A$ or $F_C$ as a consequence of the twisted period relations.
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