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On the evaluation of Salié sums

Author(s): Árpád Tóth
Journal: Proc. Amer. Math. Soc. 133 (2005), 643-645.
MSC (2000): Primary 11L05; Secondary 11F37
Posted: October 7, 2004
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Abstract: The Salié sum 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.

References:

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2.: Iwaniec, Henryk. Fourier coefficients of modular forms of half-integral weight. Invent. Math. 87 (1987), no. 2, 385-401. MR 0870736 (88b:11024)
3.: Salié, Hans. Über die Kloostermanschen Summen . (German) Math. Z. 34, 91-109, (1931).
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