Bulletin of the
Korean Mathematical Society
BKMS
Article
ALL ARTICLES
View
Bull. Korean Math. Soc. 2012; 49(6): 1327-1334
Printed November 30, 2012
https://doi.org/10.4134/BKMS.2012.49.6.1327
Copyright © The Korean Mathematical Society.
An identity on the $2m$-th power mean value of the generalized Gauss sums
Feng Liu and Quan-Hui Yang
Nanjing Normal University, Nanjing Normal University
In this paper, using analytic method and the properties of the Legendre's symbol, we prove an exact calculating formula on the $2m$-th power mean value of the generalized quadratic Gauss sums for $m\geq 2$. 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. $\bf 48$ (2011), no. 1, 9--15].
Keywords: $2m$-th power mean, exact calculating formula, generalized quadratic Gauss sums
MSC numbers: Primary 11L05; Secondary 11M20
Article Tools
Stats or Metrics
Share this article on :
Related articles in BKMS
-
On the $2k$-th power mean value of the generalized quadratic Gauss sums
2011; 48(1): 9-15
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd