Benoit Louvel
Published 2011-07-26, updated 2011-11-17Version 2
The main objective of this article is to study the asymptotic behavior of Salie sums over arithmetic progressions. We deduce from our asymptotic formula that Salie sums possess a bias of being positive. The method we use is based on 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.
Comments: 18 pages, 3 figures
Zeros of modular forms of half integral weight
On the computation of coefficients of modular forms: the reduction modulo p approach
Uniform bounds for sums of Kloosterman sums of half integral weight
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