# Siddhi Pathak (CMI)

Date

Wednesday May 15, 20242:30 pm - 3:30 pm

Location

Jeffery Hall, Room 222## Number Theory Seminar

**Wednesday, May 15th, 2024**

**Time:** 2:30 p.m. **Place:** Jeffery Hall, Room 222

**Speaker:** Siddhi Pathak (CMI)

**Title:** On the zeros of variants of Ramanujan polynomials

**Abstract:** In 2011, M. R. Murty, C. Smyth and R. Wang introduced the family of 'Ramanujan polynomials' and proved that the non-real zeros of all such polynomials lie on the unit circle. These polynomials are related to the period polynomial of standard Eisenstein series. Since then, it has been established that period polynomials associated to generalized Eisenstein series and Hecke newforms also have all their roots on the unit circle. In this talk, we discuss recent results regarding the unimodularity of zeros of certain cognate polynomials.