English

On certain bilinear sums with modular square roots and applications

Number Theory 2026-01-29 v3

Abstract

We extend bounds on additive energies of modular square roots by Dunn, Kerr, Shparlinski, Shkredov and Zaharescu and apply these results to obtain bounds on certain bilinear exponential sums with modular square roots. From here, we make partial progress on the large sieve for square moduli.

Keywords

Cite

@article{arxiv.2601.15448,
  title  = {On certain bilinear sums with modular square roots and applications},
  author = {Stephan Baier},
  journal= {arXiv preprint arXiv:2601.15448},
  year   = {2026}
}

Comments

26 pages

R2 v1 2026-07-01T09:14:53.879Z