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On the evaluation of Salié sums
Author:
Árpád Tóth
Journal:
Proc. Amer. Math. Soc. 133 (2005), 643-645
MSC (2000):
Primary 11L05; Secondary 11F37
Posted:
October 7, 2004
MathSciNet review:
2113909
Full-text PDF Free Access
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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  . 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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- Iwaniec, Henryk. Fourier coefficients of modular forms of half-integral weight. Invent. Math. 87 (1987), no. 2, 385-401. MR 0870736 (88b:11024)
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- Shimura, Goro. On modular forms of half integral weight. Ann. of Math. (2) 97, (1973), 440-481. MR 0332663 (48:10989)
- 6.
- Williams, Kenneth S. Note on Salié's sum. Proc. Amer. Math. Soc. 30, (1971), 393-394. MR 0284408 (44:1635)
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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
Posted:
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.
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