English

On a symmetric congruence and its applications

Number Theory 2007-05-23 v2

Abstract

For a large integer m,m, we obtain an asymptotic formula for the number of solutions of a certain congruence modulo mm with four variables, where the variables belong to special sets of residue classes modulo m.m. This formula are applied to obtain new information on the exceptional set of the multiplication table problem in a residue ring modulo mm and a new bound for a double trigonometric sum with an exponential function.

Keywords

Cite

@article{arxiv.math/0503164,
  title  = {On a symmetric congruence and its applications},
  author = {M. Z. Garaev and A. A. Karatsuba},
  journal= {arXiv preprint arXiv:math/0503164},
  year   = {2007}
}

Comments

19 pages

R2 v1 2026-07-22T17:16:30.369Z