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Graduate Student Number Theory Learning Seminar

Automorphic distributions and the zeros on the critical line

Doyon Kim

Location:  Via Skype
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.

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