Some congruences of Kloosterman sums and their characteristic polynomials

JOURNAL OF NUMBER THEORY

卷:133

Article

Goeloglu, Faruk¹  McGuire, Gary¹  Moloney, Richard¹ 

[1] Univ Coll Dublin, Sch Math Sci, Dublin, Ireland

关键词: Kloosterman sums;    Stickelberger's theorem;    Gross-Koblitz formula;   

DOI  :  10.1016/j.jnt.2012.09.026

来源: Elsevier

【 摘 要 】

Text. We prove two congruence results concerning Kloosterman sums over finite fields. The first result concerns the coefficients of the characteristic polynomial over Q of a Kloosterman sum, and the second result gives a characterisation of ternary Kloosterman sums modulo 27. We use methods from algebraic number theory such as Stickelberger's theorem and the Gross-Koblitz formula, as well as Fourier analysis. Video. For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=VJcB6W_PQ0s. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free