AN IDENTITY ON THE 2m-TH POWER MEAN VALUE OF THE GENERALIZED GAUSS SUMS

Title & Authors
AN IDENTITY ON THE 2m-TH POWER MEAN VALUE OF THE GENERALIZED GAUSS SUMS
Liu, Feng; Yang, Quan-Hui;

Abstract
In this paper, using analytic method and the properties of the Legendre`s symbol, we prove an exact calculating formula on the $\small{2m}$-th power mean value of the generalized quadratic Gauss sums for $\small{m{\geq}2}$. This solves a conjecture of He and Zhang [On the 2k-th power mean value of the generalized quadratic Gauss sums, Bull. Korean Math. Soc. 48 (2011), no. 1, 9-15].
Keywords
2m-th power mean;exact calculating formula;generalized quadratic Gauss sums;
Language
English
Cited by
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