Cyclicity of elliptic curves modulo primes in arithmetic progressions

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Akbal Y., Güloǧlu A. M.

Canadian Journal of Mathematics, vol.74, no.5, pp.1277-1309, 2022 (SCI-Expanded) identifier

  • 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
  • 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.