TY - JOUR
T1 - On the distribution of modular square roots of primes
AU - Shkredov, Ilya D.
AU - Shparlinski, Igor E.
AU - Zaharescu, Alexandru
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/3
Y1 - 2024/3
N2 - We use recent bounds on bilinear sums with modular square roots to study the distribution of solutions to congruences x2≡p(modq) with primes p⩽P and 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.
AB - We use recent bounds on bilinear sums with modular square roots to study the distribution of solutions to congruences x2≡p(modq) with primes p⩽P and 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.
KW - 11K38
KW - 11L07
KW - 11L20
KW - Modular square roots
KW - Prime quadratic residues
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U2 - 10.1007/s00209-024-03436-5
DO - 10.1007/s00209-024-03436-5
M3 - Article
AN - SCOPUS:85188282503
SN - 0025-5874
VL - 306
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3
M1 - 43
ER -