Colloquium abstracts

Ravi Raghunathan
IIT, Bombay
November 12, 2020

Classifying $L$-functions of (very) low degree:  I will introduce a set of Dirichlet series ${mathfrak A}^{#}$ which is known to contain the most interesting examples that arise from the theory of automorphic forms. This set is considerably larger than the extended Selberg class ${mathcal S}$ defined by Kaczorowski and Perelli. Associated to each element in this set is an invariant real number $d$ called the degree. I will try and explain how to classify elements of ${mathfrak A}^{#}$ with $d<2$. Time permitting, I will give some applications to the study of zeros of automorphic $L$-functions. Some of these results have been obtained in collaboration with R. Balasubramanian.