Department of

February 2017 March 2017 April 2017 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 2 3 4 1 5 6 7 8 9 10 11 5 6 7 8 9 10 11 2 3 4 5 6 7 8 12 13 14 15 16 17 18 12 13 14 15 16 17 18 9 10 11 12 13 14 15 19 20 21 22 23 24 25 19 20 21 22 23 24 25 16 17 18 19 20 21 22 26 27 28 26 27 28 29 30 31 23 24 25 26 27 28 29 30

Tuesday, March 14, 2017

**Abstract:** In this talk, we will see the distribution of gaps between eigenangles of Hecke operators acting on the space of cusp forms of weight $k$ and level $N$, spaces of Hilbert modular forms of weight $k = (k_1, k_2,\ldots , k_r)$ and space of primitive Maass forms of weight $0$. Moreover, we will see the following: Let $f_1$ and $f_2$ be two normalized Hecke eigenforms of weight $k_1$ and $k_2$ such that one of them is not of CM type. If the set of primes $\mathcal{P}$ such that the $p$-th coefficients of $f_1$ and $f_2$ matches has positive upper density, then $f_1$ is a Dirichlet character twist of $f_2$. The last part is a joint work with M. Ram Murty.