Cyclicity and Exponent of Elliptic Curves Modulo p in Arithmetic Progressions
Peng-Jie Wong
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 (f… Show more
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