A note on the moments of Kloosterman sums

Details A note on the moments of Kloosterman sums A note on the moments of Kloosterman sums

2011-08-03

arxiv.org/abs/1108.0746v2

Mathematics

Number Theory

8 pages, to appear in PAMS

Scientific paper

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 $S(a,1;p)\gtrless0$ as $p\rightarrow+\infty.$

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