On integral of exponent of a homogeneous polynomial

Abstract

We introduce the notion of G-hypergeometric function, where G is a complex Lie group. In the case when G is a complex torus, this notion amounts to the notion of Gelfand's A-hypergeometric function. We show that the integral $\int e^{P(x_1,...,x_n)}d{x}_1...d{x}_n$, where P is a homogeneous polynomial, is a GL(n)-hypergeometric function of algebraic SL(n)-invariants of the polynomial.

4 pages, minor corrections, a reference added

Cited by in corpus (1)

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