Alladi Ramakrishnan Hall

Prime divisors of non-zero Fourier coefficients of Hecke eigenforms (Pre-Synopsis talk)

Sunil L Naik

IMSc

The study of arithmetic properties of non-zero Fourier coefficients of Hecke eigenforms, in particular the Ramanujan $\tau$ function is an interesting topic in Number theory.

In this talk, we will give a brief overview of our recent work on non-Archimedean analogue of a question of Atkin and Serre. We will also discuss lower bounds for the number of distinct prime factors and radicals of the values of Ramanujan $\tau$ function.