On the Constants of the Lang-Trotter Conjecture for CM Elliptic Curves
Anish Ray
Anish Ray
Sep 2023
0被引用
0笔记
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摘要原文
In 2021, Daqing Wan and Ping Xi studied the equivalence of the Lang-Trotter conjecture for CM elliptic curves and the Hardy-Littlewood conjecture for primes represented by a quadratic polynomial. Wan and Xi provided an alternative description of the Lang-Trotter conjecture under the Hardy-Littlewood conjecture. They obtained an explicit constant $\overline{\omega}_{E,r}$ in the asymptotics of the Lang-Trotter conjecture. They further conjectured that this particular constant would be equal to the constant $C_{E,r}$ in the asymptotics of the original Lang-Trotter conjecture. In this paper, we verify the same for $20$ CM elliptic curves, which also establishes the equivalence of the Lang-Trotter Conjecture and the Hardy-Littlewood Conjecture with respect to $r$, for these CM elliptic curves.
