Asymptotic behaviors of Kloosterman sums

Details Asymptotic behaviors of Kloosterman sums Asymptotic behaviors of Kloosterman sums

2011-11-23

arxiv.org/abs/1111.5455v2

Mathematics

Number Theory

20 pages, Lemma 9 and some other minor errors have been revised

Scientific paper

By virtue of Chebyshev polynomials and the Rademacher-Menchov device, we investigate the asymptotic behaviors of Kloosterman sums over short intervals by making use of the Gallagher-Montgomery refinement on D.A. Burgess' estimate for character sums, and an estimate analogous of N.M. Katz's Sate-Tate law is obtained. Subsequently, we can gain some information on the sign changes and extreme values of Kloosterman sums.

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