On integral of exponent of a homogeneous polynomial

Details On integral of exponent of a homogeneous polynomial On integral of exponent of a homogeneous polynomial

2011-03-02

arxiv.org/abs/1103.0514v4

Mathematics

Algebraic Geometry

4 pages, minor corrections, a reference added

Scientific paper

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 $\int
e^{P(x_1,...,x_n)}dx_1...dx_n$, where P is a homogeneous polynomial, is a
GL(n)-hypergeometric function of algebraic SL(n)-invariants of the polynomial.

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