Israel Journal of Mathematics

, Volume 175, Issue 1, pp 349–362 | Cite as

Seventh power moments of Kloosterman sums

Article

Abstract

Evaluations of the n-th power moments S n of Kloosterman sums are known only for n ⩽ 6. We present here substantial evidence for an evaluation of S 7 in terms of Hecke eigenvalues for a weight 3 newform on ΓO(525) with quartic nebentypus of conductor 105. We also prove some congruences modulo 3, 5 and 7 for the closely related quantity T 7, where T n is a sum of traces of n-th symmetric powers of the Kloosterman sheaf.

Keywords

Dirichlet Character Symmetric Power Quadratic Character Power Moment Congruence Modulo 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  1. 1.Department of Mathematics, 0112University of California at San DiegoLa JollaUSA

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