Yujiao Jiang (Shandong University): Bombieri-Vinogradov theorem for $GL(n)$ automorphic $L$-functions

Abstract: The celebrated Bombieri-Vinogradov theorem states that the primes up to $x$ in arithmetic progressions modulo $q$ are well-distributed for all $q\leq x^{1/2} / \log^B x$, which shows that the GRH is true on average. In this talk, we present a unconditional generalization of Bombieri-Vinogradov theorem in the $GL(n)$ automorphic context. In particular, we give the same quality as the result of Bombieri-Vinogradov when $n\leq 4$. As applications, we also discuss some shifted convolution problems at integers and primes. This is recent joint work with Guangshi Lü, Jesse Thorner and Zihao Wang.

The link for the talk is https://zoom.us/j/94752830725, the password is the order of $\mathrm{SL}_2(\mathbb{F}_{97})$.