Title: Lang-Trotter Conjecture for CM Elliptic Curves
Abstract: For any elliptic curve $E$ over $\mathbf{Q}$ and any non-zero integer $r$, the Lang-Trotter conjecture has predicted the asymptotic behaviours of the number of good primes $p\leqslant x$, denoted by $\pi_{E,r}(x)$, such that the Frobenius trace of $E$ at $p$ is equal to the given integer $r$. Quite recently, we are able to prove an estimate for $\pi_{E,r}(x)$ which confirms the upper bound part of the conjecture for CM elliptic curves. Moreover, intimate connections of this conjecture and Hardy-Littlewood conjecture can also be established to characterize the shape of the Lang-Trotter constant in $\pi_{E,r}(x)$. This is based on the joint work with Daqing Wan (in progress).
Speaker：Xi Ping (Xi’an Jiaotong University)
Time: 15:00-16:00 am, April 15, 2021
Place：Tencent Meeting，Meeting ID：296 101 721
