A NEW MEAN VALUE RELATED TO D. H. LEHMER'S PROBLEM AND KLOOSTERMAN SUMS

Title & Authors
A NEW MEAN VALUE RELATED TO D. H. LEHMER'S PROBLEM AND KLOOSTERMAN SUMS
Han, Di; Zhang, Wenpeng;

Abstract
Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with $\small{1{\leq}a{\leq}q-1}$, it is clear that the exists one and only one b with $\small{0{\leq}b{\leq}q-1}$ such that $\small{ab{\equiv}c}$ (mod q). Let N(c, q) denote the number of all solutions of the congruence equation $\small{ab{\equiv}c}$ (mod q) for $\small{1{\leq}a}$, $\small{b{\leq}q-1}$ in which a and $\small{\bar{b}}$ are of opposite parity, where $\small{\bar{b}}$ is defined by the congruence equation $\small{b\bar{b}{\equiv}1}$ (modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving $\small{(N(c,q)-\frac{1}{2}{\phi}(q))}$ and Kloosterman sums, and give a sharper asymptotic formula for it.
Keywords
D. H. Lehmer's problem;error term;Kloosterman sums;hybrid mean value;asymptotic formula;
Language
English
Cited by
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