On the Lang-Trotter conjecture for a class of non-generic abelian surfaces

Abstract

In the present article, we formulate a conjectural uniform error term in the Chebotarev-Sato-Tate distribution for abelian surfaces $\mathbb{Q}$-isogenous to a product of not $\overline{\mathbb{Q}}$-isogenous non-CM-elliptic curves, established by the author in \cite[Theorem 1.1]{Amri22}. As a consequence, we provide a direct proof to the generalized Lang-Trotter conjecture recently formulated and studied in \cite{Chen}.

10 pages, comments are welcome!

References in corpus (2)

• Bounds for the distribution of the Frobenius traces associated to products of non-CM elliptic curves
• Chebotarev-Sato-Tate distribution for abelian surfaces potentially of ${\mathrm{GL}}_2$-type