English

Bounds for the Lang-Trotter conjectures

Number Theory 2015-09-01 v1

Abstract

For a non-CM elliptic curve EE defined over the rationals, Lang and Trotter made very deep conjectures concerning the number of primes pxp\leq x for which ap(E)a_p(E) is a fixed integer (and for which the Frobenius field at pp 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.

Keywords

Cite

@article{arxiv.1508.07682,
  title  = {Bounds for the Lang-Trotter conjectures},
  author = {David Zywina},
  journal= {arXiv preprint arXiv:1508.07682},
  year   = {2015}
}

Comments

To appear in CRM Proceedings Series, published by the AMS as part of the Contemporary Mathematics Series, dedicated to Ram Murty's 60th birthday conference

R2 v1 2026-06-22T10:44:52.574Z