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- Title
Cyclicity and Exponent of Elliptic Curves Modulo p in Arithmetic Progressions.
- Authors
Wong, Peng-Jie
- Abstract
In this article, we study the cyclicity problem of elliptic curves |$E/\mathbb{Q}$| modulo primes in a given arithmetic progression. We extend the recent work of Akbal and Güloğlu by proving an unconditional asymptotic for such a cyclicity problem over arithmetic progressions for elliptic curves E , which also presents a generalization of the previous works of Akbary, Cojocaru, M.R. Murty, V.K. Murty and Serre. In addition, we refine the conditional estimates of Akbal and Güloğlu, which gives log-power savings (for small moduli) and consequently improves the work of Cojocaru and M.R. Murty. Moreover, we study the average exponent of E modulo primes in a given arithmetic progression and obtain several conditional and unconditional estimates, extending the previous works of Freiberg, Kim, Kurlberg and Wu.
- Subjects
ELLIPTIC curves; ARITHMETIC series; EXPONENTS
- Publication
Quarterly Journal of Mathematics, 2024, Vol 75, Issue 2, p757
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/haae029