Chen, HaoJones, NathanSerban, Vlad2022-04-112022-04-112022-04-112022-03-2110.1007/s11139-021-00543-3https://infoscience.epfl.ch/handle/20.500.14299/187031WOS:000771636700001Inspired 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 that are not (Q) over bar -isogenous. 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.Mathematicselliptic curvesabelian surfacesgalois representationsmodulestext::journal::journal article::research article