Hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums

Huaning Liu; Wenpeng Zhang

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J. Korean Math. Soc. 2007; 44(1): 11-24

Printed January 1, 2007

Hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums

Huaning Liu and Wenpeng Zhang

Northwest University, Northwest University

Abstract

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Abstract

The main purpose of this paper is to use the properties of primitive characters, Gauss sums and Ramanujan's sum to study the hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums, and give two asymptotic formulae.

Keywords: Bernoulli numbers, Kloosterman sums, Gauss sums

MSC numbers: 11B68, 11L05