Alladi Ramakrishnan Hall

Zeros of period polynomials of Hecke eigenforms

Mrityunjoy Charan

IMSc

The period polynomial of a cusp form of level 1 is the generating function of its critical L-values. The Eichler-Shimura theorem says that the space of all cusp forms of level 1 is isomorphic to the space of all odd period polynomials. It follows that a cusp form is uniquely defined by its period polynomial (in fact, the odd part would be sufficient). In the light of the theorem of Eichler and Shimura, studying the zeros of period polynomials is as natural as studying the zeros of cusp forms. In this seminar, we will discuss the zeros of period polynomials of Hecke eigenforms.