论文标题
非CM椭圆曲线产物的Lang-Trotter猜想
The Lang-Trotter Conjecture for products of non-CM elliptic curves
论文作者
论文摘要
受Lang-Trotter在$ \ Mathbb {Q} $上定义的椭圆形曲线的质量密度的工作的启发，并通过随后对Cojocaru-Davis-Silverberg-Stange的概括为普通的Abelian品种的类似问题，我们研究了Abelian curvise的类似问题，我们研究了Abelos cur的类似问题。 $ \ mathbb {q} $。我们制定相应的猜想渐近线，提供上限，并明确计算（当椭圆曲线位于薄的集合外）时，出现在渐近线中的算术具有重要意义的常数。这使我们能够为猜想提供计算证据。
Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over $\mathbb{Q}$ 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 $\mathbb{Q}$. 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.
