Maga Péter: The sup-norm problem for automorphic cusp forms of PGL(n,Z[i])

Absztrakt: It was proven by Sarnak that L^2-normalized eigenfunctions f of invariant differential operators over a locally symmetric space X can be estimated by a certain power (expressed in terms of invariants of X) of the Laplace eigenvalue of f (under some compactness conditions, i.e. X is compact or f is restricted to a compact subset of X). The sup-norm problem of automorphic forms asks whether a saving over this generic bound is available if f is further an eigenfunction of the Hecke operators. In our series of talks, we prove that such a saving exists if X=PGL(n,Z[i]) \ PGL(n,C) / PU(n). Joint work with Gergely Zábrádi.

For Zoom access please contact Andras Biro (biro.andras[a]renyi.hu).