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Cyclicity of elliptic curves modulo primes in arithmetic progressions

Part of: Multiplicative number theory Arithmetic algebraic geometry Algebraic number theory: global fields

Published online by Cambridge University Press:  03 May 2021

Yıldırım Akbal  and
Ahmet M. Güloğlu
Yıldırım Akbal
Affiliation:
Department of Mathematics, Atılım University, 06830 Gölbaşı, Ankara, Turkey e-mail: yildirim.akbal@atilim.edu.tr
Ahmet M. Güloğlu*
Affiliation:
Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey
*
e-mail: guloglua@fen.bilkent.edu.tr
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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.

Keywords

Cyclicity conjecturereduction of elliptic curves modulo primesprimes in arithmetic progressionsChebotarev density theorem

MSC classification

Primary: 11G05: Elliptic curves over global fields
Secondary: 11N13: Primes in progressions 11N36: Applications of sieve methods 11N45: Asymptotic results on counting functions for algebraic and topological structures 11R45: Density theorems
Type
Article
Information
Canadian Journal of Mathematics , Volume 74 , Issue 5 , October 2022 , pp. 1277 - 1309
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Copyright
© Canadian Mathematical Society 2021

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