Summer 2024
Time & Location: All talks are on Wednesdays in DW 102 at 2:00 PM unless otherwise noted.
Organizer: Victor H. Moll, and Olivia Beckwith
June 18
Title: Mordell-Tornheim zeta functions and functional equations of Herglotz-Zagier type functions
Atul Dixit - IIT Gandhinagar
Abstract: In this talk, we will present our recent results on a generalization of the Mordell-Tornheim zeta function, in particular, the two- and three-term functional equations that it satisfies. This function is intimately connected with a new extension of the Herglotz-Zagier function F(x) . Radchenko and Zagier recently studied arithmetic properties of F(x), in particular, their special values and functional equations coming from Hecke operators. One of our results on this extension not only gives the well-known two-term functional equation of F(x) as a special case but also those of Ishibashi functions, which were sought after for over twenty years. A grand generalization of an integral considered by Herglotz as well as its companion due to Muzzaffar and Williams, which involves generalized Fekete polynomials and character polylogarithms, is obtained. By deriving a functional equation for this generalization, we are able to get doubly infinite families of functional equations whose two special cases were recently obtained by Choie and Kumar. This is joint work with Sumukha Sathyanarayana and N. Guru Sharan.
Location: Gibson Hall Room 310
Time: 3:30-4:30pm
