On the $r$-th hyper-Kloosterman sums and its hybrid mean value

Tianping Zhang; Wenpeng Zhang

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2006; 43(6): 1199-1217

Printed November 1, 2006

On the $r$-th hyper-Kloosterman sums and its hybrid mean value

Tianping Zhang and Wenpeng Zhang

Northwest University, Northwest University

Abstract

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Abstract

The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the $r$-th hyper-Kloosterman sums $Kl(h,k+1,r;q)$ and the hyper Cochrane sums $C(h,q;m,k),$ and give an interesting mean value formula.

Keywords: hyper-Kloosterman sums, hyper Cochrane sums, hybrid mean value

MSC numbers: 11N37, 11F20