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

2022/11/18 by Mohammed Amin Amri, Amri, Mohammed Amin
Mathematics · Social Sciences · #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Partial Differential Equations #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2211.10523

openalex publication_date 2022/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present article, we formulate a conjectural uniform error term in the Chebotarev-Sato-Tate distribution for abelian surfaces ℚ-isogenous to a product of not 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 \citeChen.

Related

• The Lang-Trotter Conjecture for products of non-CM elliptic curves
• A refined version of the Lang-Trotter Conjecture
• Lang-Trotter and Sato-Tate Distributions in Single and Double Parametric Families of Elliptic Curves
• On the Sato-Tate conjecture for non-generic abelian surfaces
• On Effective Sato-Tate Distributions for Surfaces Arising from Products of Elliptic Curves