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D. H. LEHMER PROBLEM OVER HALF INTERVALS

  • Xu, Zhefeng
  • Published : 2009.05.01

Abstract

Let $q\;{\geq}\;3$ 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 $bc\;{\equiv}\;a$ (mod q), $1\;{\leq}\;b$, $c\;{\leq}\;{\frac{q-1}{2}}$ and with b, c having different parity. The main purpose of this paper is to study the sum ${\sum}^{'q}_{a=1}\;\(N(a,\;q)\;-\;\frac{{\phi}(q)}{8}\)^2$ and obtain a sharp asymptotic formula.

Keywords

error term;mean value;asymptotic formula

References

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Cited by

  1. Modular hyperbolas vol.7, pp.2, 2012, https://doi.org/10.1007/s11537-012-1140-8