## Lethbridge Number Theory and Combinatorics Seminar: Nathan Ng

• Date: 01/29/2018
Speaker(s):
Nathan Ng (University of Lethbridge)
Location:

University of Lethbridge

Topic:

Mean values of long Dirichlet polynomials

Description:

A Dirichlet polynomial is a function of the form $A(t)=\sum_{n \le N} a_n n^{-it}$ where $a_n$ is a complex sequence, $N \in \mathbb{N}$, and $t \in \mathbb{R}$.  For $T \ge 1$, the mean values$$\int_{0}^{T} |A(t)|^2 \, dt$$play an important role in the theory of L-functions.  I will discuss work of Goldston and Gonek on how to evaluate these integrals in the case that $T < N < T^2$.  This will depend on the correlation sums $\sum_{n \le x} a_n a_{n+h} \text{ for } h \in \mathbb{N}.$If time permits, I will discuss a conjecture of Conrey and Keating in the case that $a_n$ corresponds to a generalized divisor function and $N > T$.

Organizers:

Other Information:

Time: 12:00-12:50pm

Location: B543 University Hall