The next talk is by Rahul Kumar, Fulbright-Nehru Postdoctoral Fellow, Penn State University. The announcement is as follows.
Title: Arithmetic properties of the Herglotz-Zagier-Novikov function
Speaker: Rahul Kumar (Penn State University)
When: Apr 27, 2023, 4:00 PM- 5:00 PM IST
Where: Zoom: Write to sfandnt@gmail.com for a link
Live Link: https://youtube.com/live/5iJRbNZOksM?feature=share
Abstract
The Kronecker limit formulas are concerned with the constant term in the Laurent series expansion of certain Dirichlet series at $s=1$. Various special functions appear in Kronecker limit formulas; one of them is \emph{Herglotz function}. Recently, Radchenko and Zagier extensively studied the properties of the Herglotz function, such as its special values, connection to Stark's conjecture, etc. This function appeared in the work of Herglotz, and Zagier. After providing an overview of the history of this research area, we will discuss the arithmetic properties of a Herglotz-type function that appears in a Kronecker limit formula derived by Novikov. For example, we will present the two- and three-term functional equations satisfied by it along with its special values. This is joint work with Professor YoungJu Choie.
