Bounds for the Lang-Trotter conjectures

2015/08/31 by David Zywina, Zywina, David
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1508.07682

openalex publication_date 2015/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a non-CM elliptic curve E defined over the rationals, Lang and Trotter made very deep conjectures concerning the number of primes p≤ x for which a_p(E) is a fixed integer (and for which the Frobenius field at p is a fixed imaginary quadratic field). Under GRH, we use a smoothed version of the Chebotarev density theorem to improve the best known Lang-Trotter upper bounds of Murty, Murty and Saradha, and Cojocaru and David.

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