Author:
Shkredov Ilya D.,Shparlinski Igor E.,Zaharescu Alexandru
Abstract
AbstractWe use recent bounds on bilinear sums with modular square roots to study the distribution of solutions to congruences $$x^2 \equiv p \pmod q$$
x
2
≡
p
(
mod
q
)
with primes $$p\leqslant P$$
p
⩽
P
and $$q \leqslant Q$$
q
⩽
Q
. This can be considered as a combined scenario of Duke, Friedlander and Iwaniec with averaging only over the modulus q and of Dunn, Kerr, Shparlinski and Zaharescu with averaging only over p.
Funder
University of New South Wales
Publisher
Springer Science and Business Media LLC