English

Linear Congruences with Ratios

Number Theory 2015-03-12 v1

Abstract

We use new bounds of double exponential sums with ratios of integers from prescribed intervals to get an asymptotic formula for the number of solutions to congruences j=1najxjyj1a0(modp), \sum_{j=1}^n a_j x_jy_j^{-1} \equiv a_0 \pmod p, with variables from rather general sets.

Keywords

Cite

@article{arxiv.1503.03196,
  title  = {Linear Congruences with Ratios},
  author = {Igor E. Shparlinski},
  journal= {arXiv preprint arXiv:1503.03196},
  year   = {2015}
}
R2 v1 2026-06-22T08:49:39.373Z