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arXiv · 1508.07682

Bounds for the Lang-Trotter conjectures

David Zywina
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Abstract

For a non-CM elliptic curve $E$ defined over the rationals, Lang and Trotter made very deep conjectures concerning the number of primes $p\leq x$ 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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David Zywina. 2015-08-31. Bounds for the Lang-Trotter conjectures. https://arxiv.org/abs/1508.07682

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