TY - JOUR
T1 - Poisson Behavior for Chains of Small Quadratic Non-Residues
AU - Basak, Debmalya
AU - Nath, Kunjakanan
AU - Zaharescu, Alexandru
PY - 2024/2/1
Y1 - 2024/2/1
N2 - It is known that under the Generalized Riemann Hypothesis, the smallest quadratic non-residue modulo a prime p is less than or equal to (log p)2. In ranges slightly larger, of size (log p)A with A > 2, we consider chains of r consecutive quadratic non-residues. We prove unconditionally that for almost all primes p in short intervals, these chains exhibit Poisson behavior.
AB - It is known that under the Generalized Riemann Hypothesis, the smallest quadratic non-residue modulo a prime p is less than or equal to (log p)2. In ranges slightly larger, of size (log p)A with A > 2, we consider chains of r consecutive quadratic non-residues. We prove unconditionally that for almost all primes p in short intervals, these chains exhibit Poisson behavior.
UR - http://www.scopus.com/inward/record.url?scp=85186098910&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85186098910&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnad168
DO - 10.1093/imrn/rnad168
M3 - Article
SN - 1073-7928
VL - 2024
SP - 3356
EP - 3390
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 4
M1 - rnad168
ER -