Article ID Journal Published Year Pages File Type
4593799 Journal of Number Theory 2014 10 Pages PDF
Abstract

Using elementary methods, we obtain an explicit formula for the fourth power mean∑m=1q′∑χmodq|∑a=1q′χ(a)e(mak+naq)|4 for arbitrary positive integer k  , where e(y)=e2πiye(y)=e2πiy, χ is a Dirichlet character modulo q   and ∑a=1q′ denotes the summation over all a   such that (a,q)=1(a,q)=1. This improves H.N. Liu's result by averting the restriction (k,q)=1(k,q)=1.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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