Seventh Power Moments of Kloosterman Sums
نویسنده
چکیده
Evaluations of the n-th power moments Sn of Kloosterman sums are known only for n 6 6. We present here substantial evidence for an evaluation of S7 in terms of Hecke eigenvalues for a weight 3 newform on Γ0(525) with quartic nebentypus of conductor 105. We also prove some congruences modulo 3, 5 and 7 for the closely related quantity T7, where Tn is a sum of traces of n-th symmetric powers of the Kloosterman sheaf.
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