Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593799 | Journal of Number Theory | 2014 | 10 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chen Hua, Ai Xiaochuan, Cai Guangxing,