D. H. LEHMER PROBLEM OVER HALF INTERVALS

Title & Authors
D. H. LEHMER PROBLEM OVER HALF INTERVALS
Xu, Zhefeng;

Abstract
Let $\small{q\;{\geq}\;3}$ be an odd integer and a be an integer coprime to q. Denote by N(a, q) the number of pairs of integers b, c with $\small{bc\;{\equiv}\;a}$ (mod q), $\small{1\;{\leq}\;b}$, $\small{c\;{\leq}\;{\frac{q-1}{2}}}$ and with b, c having different parity. The main purpose of this paper is to study the sum $\small{{\sum}^{$ and obtain a sharp asymptotic formula.
Keywords
error term;mean value;asymptotic formula;
Language
English
Cited by
1.
Modular hyperbolas, Japanese Journal of Mathematics, 2012, 7, 2, 235
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