Exponential sums and finite field $A$-hypergeometric functions

Alan Adolphson

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arXiv · 1210.6400

Exponential sums and finite field $A$-hypergeometric functions

Alan Adolphson

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Abstract

We define finite field $A$-hypergeometric functions and show that they are Fourier expansions of families of exponential sums on the torus. For an appropriate choice of $A$, our finite field $A$-hypergeometric function can be specialized to the finite field ${}_kF_{k-1}$-hypergeometric function defined by McCarthy.

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Alan Adolphson. 2012-10-23. Exponential sums and finite field $A$-hypergeometric functions. https://arxiv.org/abs/1210.6400

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