Seminars & Colloquia Calendar
Automorphic distributions and the zeros on the critical line
Location: Via Skype https://join.skype.com/Wa2dqeBTH0PC
Date & time: Wednesday, 06 May 2020 at 9:20AM - 10:20AM
Abstract: The automorphic distribution attached to a classical modular form F(z) is defined as the boundary values of F:
tau(x)=lim (y to 0+) F(x+iy). In this talk I will take the modular discriminant Delta(z) as an example and introduce some of the nice properties of its automorphic distribution. We can define the Mellin transform of tau(x) and use it to derive the functional equation of L(s, Delta). I will explain how the automorphic distributions can be used to prove that there are infinitely many zeros of L(s, Delta) on the critical line.