2020/06/19 by Hao Chen, Chen, Hao, Nathan D. Jones +3
Arts and Humanities · Mathematics · #11F80 #11G05 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #North African History and Literature #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2006.11269
openalex publication_date 2020/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over ℚ and by the subsequent generalization of Cojocaru-Davis-Silverberg-Stange to generic abelian varieties, we study the analogous question for abelian surfaces isogenous to products of non-CM elliptic curves over ℚ. We formulate the corresponding conjectural asymptotic, provide upper bounds, and explicitly compute (when the elliptic curves lie outside a thin set) the arithmetically significant constants appearing in the asymptotic. This allows us to provide computational evidence for the conjecture.