On a Kind of Dirichlet Character Sums

Abstract

Let p≥3 be a prime and let χ denote the Dirichlet character modulo p. For any prime q with q<p, define the set Eq,p=a∣1≤a,a-≤p,aa-≡1modp and a≡a-modq. In this paper, we study a kind of mean value of Dirichlet character sums ∑a≤p a∈Eq,pχ(a), and use the properties of the Dirichlet L-functions and generalized Kloosterman sums to obtain an interesting estimate.