The first moment of Salié sums

The main objective of this article is to study the asymptotic behavior of Salié sums over arithmetic progressions. We deduce from our asymptotic formula that Salié sums possess a bias towards being positive. The method we use is based on the Kuznetsov formula for modular forms of half-integral weigh...

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Bibliographic Details
Published in:Monatshefte für Mathematik 2012-12, Vol.168 (3-4), p.523-543
Main Author: Louvel, Benoît
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:The main objective of this article is to study the asymptotic behavior of Salié sums over arithmetic progressions. We deduce from our asymptotic formula that Salié sums possess a bias towards being positive. The method we use is based on the Kuznetsov formula for modular forms of half-integral weight. Moreover, in order to develop an explicit formula, we are led to determine an explicit orthogonal basis of the space of modular forms of half-integral weight.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-011-0366-5