**Title: **Asymptotic formula for ideal counting function in short intervals

**Speaker: **Zhishan Yang, School of Mathematics and Statistics, Qingdao University

**Abstract: **Let K be a finite abelian extension over $\mathbb{Q}$, $a_K(n)$ is the number of non-zero integral ideals with norm $n$. Since the main term of the sum $\sum\limits_{n\leq x}{a_K(n)}$ nearly contains all the invariants of $K$, it is interesting to study its asymptotic formula. In this topic, By using Motohashi’s method and zero density for Zeta function, we'll give an asymptotic formula for ideal counting function in short intervals.

**Time/Venue: **14:00-15:00 21/11/2019 B819