报告题目：Upper bounds for the distribution of Frobenius traces of abelian varieties

报告人：Dr. Wang Tian (Max Planck Institute of Mathematics in Bonn)

时间：2023年2月8日（星期三）上午9:00-10:00

腾讯会议153-916-814，密码 230208

摘要：Let A be an abelian variety of dimension g defined over the rationals. Let t be an arbitrary integer. We denote by $\pi_A(x, t)$ the number of primes up to x, such that the Frobenius trace of A equals to t. The growth of the function $\pi_A(x, t)$ was first studied by Lang and Trotter in 1976 for elliptic curves, and generalized by Cojocaru, Davis, Silverberg, and Stange in 2016 and Chen, Jones, and Serban for higher dimensional abelian varieties. In the talk, I will present the latest upper bound for $\pi_A(x, t)$ under the Generalized Riemann Hypothesis for Dedekind zeta functions. The bound recovers the upper bound for a non-CM elliptic curve and gives the best known result for an abelian variety with $g \geq 2$. This is in joint work with A.C. Cojocaru.