On the evaluation of Salié sums

Tóth, Árpád

doi:10.1090/S0002-9939-04-07768-8

On the evaluation of Salié sums
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by Árpád Tóth PDF

Proc. Amer. Math. Soc. 133 (2005), 643-645 Request permission

Abstract:

The Salié sum $S(m,n;c)$ can be evaluated as the product of a Gauss sum and an exponential sum involving square roots of $mn \bmod {c}$. We give a new proof of this fact that can simultaneously handle a twisted version of these sums that arise in the theory of half-integral weight modular forms.

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