Bounds for the Lang-Trotter conjectures
Number Theory
2015-09-01 v1
Abstract
For a non-CM elliptic curve defined over the rationals, Lang and Trotter made very deep conjectures concerning the number of primes for which is a fixed integer (and for which the Frobenius field at 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