Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2011; 48(1): 9-15

Printed January 1, 2011

https://doi.org/10.4134/BKMS.2011.48.1.9

Copyright © The Korean Mathematical Society.

On the $2k$-th power mean value of the generalized quadratic Gauss sums

Yanfeng He and Wenpeng Zhang

Yan'an University, Northwest University

Abstract

The main purpose of this paper is using the elementary and analytic methods to study the properties of the $2k$-th power mean value of the generalized quadratic Gauss sums, and give two exact mean value formulae for $k=3$ and $4$.

Keywords: generalized quadratic Gauss sums, $2k$-th power mean value, calculating formula, identity

MSC numbers: Primary 11M20