Spectral Theory of the Riemann Zeta function - 1

by Lasse Grimmelt

Monday 18 Mar 2024, 11:00 → 12:00 Europe/Zurich

Sitzungszimmer (MI)

In 1994 Motohashi proved in his ground-breaking work that the fourth moment of Riemann's Zeta function admits an interpretation as a third central moment of L functions summed over a basis of Maaß-cusp as well as holomorphic modular forms. The original proof uses sums of Kloosterman sums and the spectral interpretation arises via Kuznetsov's formula. In 2007, Bruggeman and Motohashi gave a much more direct proof that completely dispenses with Kloosterman sums. In this series of talks we will outline this new approach and obtain an intuitive understanding of why one should expect Motohashi's spectral expansion to have the shape it has.