Cyclicity of elliptic curves modulo primes in arithmetic progressions
Canadian Journal of Mathematics, vol.74, no.5, pp.1277-1309, 2022 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 74 Issue: 5
- Publication Date: 2022
- Doi Number: 10.4153/s0008414x21000237
- Journal Name: Canadian Journal of Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Page Numbers: pp.1277-1309
- Keywords: Chebotarev density theorem., Cyclicity conjecture, primes in arithmetic progressions, reduction of elliptic curves modulo primes
- Open Archive Collection: AVESIS Open Access Collection
- TED University Affiliated: Yes
Abstract
We consider the reduction of an elliptic curve defined over the rational numbers modulo primes in a given arithmetic progression and investigate how often the subgroup of rational points of this reduced curve is cyclic.