Venue
SMS Conference Room (via GoogleMeet)
Speaker
Sudhir Pujahari
Affiliation
The University of Hong Kong
Title
Arithmetic and statistics of sums of eigenvalues of Hecke operators
In the first part of the talk, we will discuss briefly the theory of Equidistribution. In the second part of the talk we will see the distribution of gaps between eigenvalues of Hecke operators in both horizontal and vertical settings. Moreover, we will deduce a stronger version of multiplicity one theorem for the space of cusp forms of weight k and level N from the joint Sato-Tate conjecture. This is a joint work with M. Ram Murty. Finally, using recent developments in the theory of l-adic Galois representations we will study the normal number of prime factors of sums of Fourier coefficients of eigenforms. The final part is a joint work with M. Ram Murty and V. Kumar Murty.