Alladi Ramakrishnan Hall

On arithmetic behavior of Hecke eigenvalues of cusp forms

Biplab Paul

IMSc

It is well known that Hecke eigenvalues of elliptic cusp forms as well as Siegel cusp forms which are not in the Maass space
changes sign infinitely often. In this talk, we will talk about simultaneous sign changes of these Hecke eigenvalues. Moreover, we will show that the Hecke eigenvalues of Siegel cusp forms which are in the Maass space
are always positive. We will derive
Omega results for these eigenvalues.