A note on the moments of Kloosterman sums

Xi, Ping; Yi, Yuan

doi:10.1090/S0002-9939-2012-11374-7

A note on the moments of Kloosterman sums
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by Ping Xi and Yuan Yi PDF

Proc. Amer. Math. Soc. 141 (2013), 1233-1240 Request permission

Abstract:

In this note, we deduce an asymptotic formula for even power moments of Kloosterman sums based on the important work of N. M. Katz on Kloosterman sheaves. In a similar manner, we can also obtain an upper bound for odd power moments. Moreover, we shall give an asymptotic formula for odd power moments of absolute Kloosterman sums. Consequently, we find that there are infinitely many $a\bmod p$ such that $S(a,1;p)\gtrless 0$ as $p\rightarrow +\infty .$

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