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Seventh power moments of Kloosterman sums

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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.

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  1. Department of Mathematics, 0112, University of California at San Diego, La Jolla, CA, 92093-0112, USA

    Ronald Evans

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  1. Ronald Evans
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Correspondence to Ronald Evans.

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Evans, R. Seventh power moments of Kloosterman sums. Isr. J. Math. 175, 349–362 (2010). https://doi.org/10.1007/s11856-010-0014-0

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  • DOI: https://doi.org/10.1007/s11856-010-0014-0

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