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Exponential sums and finite field $A$-hypergeometric functions (1210.6400v1)
Published 23 Oct 2012 in math.NT
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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