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Joint IAS/Princeton University Number Theory Seminar

Taking the Hecke algebra to its limits

We parametrise elements in the full Hecke algebra in a way such that the parametrisation represents a generic automorphic form. By convolving, we then arrive at pre-trace formulas which are modular in three variables. From here, various identities for higher moments may be derived. We give applications to the sup-norm and fourth-norm of holomorphic Hecke eigenforms as well as Hecke-Maass forms on and furthermore outline future work on higher moments of periods and quantum variance. This is joint work with Ilya Khayutin.


Raphael Steiner

Speaker Affiliation

Member, School of Mathematics



Event Series

Date & Time
September 12, 2019 | 4:305:30pm


Simonyi Hall 101