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arXiv · 2211.10523

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

Mohammed Amin Amri
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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}.

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Mohammed Amin Amri. 2022-11-18. On the Lang-Trotter conjecture for a class of non-generic abelian surfaces. https://doi.org/10.1007/s11139-024-00884-9

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