On integral of exponent of a homogeneous polynomial

2011/03/02 by A. Stoyanovsky, Alexander Roi Stoyanovsky, Stoyanovsky, A. · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #hep-th #math-ph #math.AG #math.MP

paper · pdf · doi:10.48550/arxiv.1103.0514

4 pages, minor corrections, a reference added

openalex publication_date 2011/03/02 · arxiv created 2011/03/20 · arxiv updated 2011/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ∫ e^{P(x₁,...,x_n)}dx₁...dx_n, where P is a homogeneous polynomial, is a GL(n)-hypergeometric function of algebraic SL(n)-invariants of the polynomial.

Citations

• Hypergeometric functions on reductive groups

Cited by

• Level sets and non Gaussian integrals of positively homogeneous functions
• Beyond the Gaussian II : A Mathematical Experiment

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