Hypergeometric polynomials are optimal

D. V. Bogdanov; T. M. Sadykov

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arXiv · 1506.00503

Hypergeometric polynomials are optimal

D. V. Bogdanov·T. M. Sadykov

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Abstract

With any integer convex polytope $P\subset\midR^n$ we associate a multivariate hypergeometric polynomial whose set of exponents is $\midZ^{n}\cap P.$ This polynomial is defined uniquely up to a constant multiple and satisfies a holonomic system of partial differential equations of Horn's type. We prove that the zero locus of any such polynomial is optimal in the sense of Forsberg-Passare-Tsikh.

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D. V. Bogdanov, T. M. Sadykov. 2015-06-01. Hypergeometric polynomials are optimal. https://arxiv.org/abs/1506.00503

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