On the distribution of modular square roots of primes
Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu

TL;DR
This paper investigates how solutions to quadratic congruences involving primes and moduli are distributed, using advanced bounds on bilinear sums with modular square roots, blending previous approaches with new averaging techniques.
Contribution
It introduces new bounds on bilinear sums with modular square roots to analyze the distribution of solutions to quadratic congruences involving primes and moduli.
Findings
Derived bounds improve understanding of solution distribution
Unified previous approaches with new averaging techniques
Enhanced estimates for primes and moduli in quadratic congruences
Abstract
We use recent bounds on bilinear sums with modular square roots to study the distribution of solutions to congruences with primes and integers . This can be considered as a combined scenario of Duke, Friedlander and Iwaniec with averaging only over the modulus and of Dunn, Kerr, Shparlinski and Zaharescu with averaging only over .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic Number Theory Research · History and Theory of Mathematics
