ON THE GENERALIZATION OF THE D. H. LEHMER PROBLEM AND ITS MEAN VALUE
Let p be an odd prime and c be a quadratic residue modulo p. Denote by the number of integers a, b with with a, b are quadratic residues modulo p having different parity. The main purpose of this paper is using the estimates for character sums and the mean value theorem of Dirichlet L-function to deduce an asymptotic for where denotes the set of all quadratic residues modulo p.
D. H. Lehmer generalized problem, Dirichlet L-functions, mean value.