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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the evaluation of Salié sums


Author: Árpád Tóth
Journal: Proc. Amer. Math. Soc. 133 (2005), 643-645
MSC (2000): Primary 11L05; Secondary 11F37
Published electronically: October 7, 2004
MathSciNet review: 2113909
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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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Additional Information

Árpád Tóth
Affiliation: Departament of Analysis, Eötvös Lórand University, Pázmány Péter Sétány 1/c, H-1117 Budapest, Hungary
Email: toth@cs.elte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07768-8
PII: S 0002-9939(04)07768-8
Received by editor(s): October 6, 2003
Published electronically: October 7, 2004
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.