An identity on the $2m$-th power mean value of the generalized Gauss sums

Details An identity on the $2m$-th power mean value of the generalized Gauss sums An identity on the $2m$-th power mean value of the generalized Gauss sums

2011-07-13

arxiv.org/abs/1107.2470v1

Mathematics

Number Theory

12pages

Scientific paper

In this paper, using combinatorial and analytic methods, 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. 48 (2011), No.1, 9-15].

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