Dr. Aditi Savalia will give a number theory seminar on Thursday, December 26 at 10:00 a.m. in Ramanujan Hall.

Title: Approximate functional equation for $\zeta(s)\zeta(s-\alpha)$
Abstract:
The Riemann zeta function is defined by
$\zeta(s)=\sum_{n}1/n^s=\prod_{p-prime}(1-1/p^s)^{-1}$, for $Re(s)>1$.
Further, it can be analytically continued to the whole complex plane
except for a simple pole at $s=1$. The behavior of this function is
fascinating in the critical strip $0<Re(s)<1$. One way to understand this
is by truncating the series or product to finite terms and studying its
relation with the zeta function, known as the approximate functional
equation. In this talk, we will discuss identities related to approximate
functional equation for $\zeta(s)\zeta(s-\alpha)$, for some complex number
$\alpha$.