Israel Journal of Mathematics

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

Seventh power moments of Kloosterman sums



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.


Dirichlet Character Symmetric Power Quadratic Character Power Moment Congruence Modulo 
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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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