Hall 123

Eichler integrals, Ramanujan-type identities and period polynomials

Siddhi Pathak

CMI

One of the many striking formulas suggested by Ramanujan include an identity connecting the value of the Riemann zeta-function at odd positive integers, a Lambert series and a polynomial with product of Bernoulli numbers as coefficients. This identity has garnered a lot of interest, with the modern perspective being that it is a special case of the transformation formula for the Eichler integral of an Eisenstein series in terms of the corresponding period polynomial. In this talk, we expand upon this approach and indicate generalizations of this idea that have appeared in recent times.