Dimitrios Chatzakos: Mean values and quantum variance for degenerate Eisenstein series of higher rank

Abstract:

 The Quantum unique ergodicity conjecture for the classical Eisenstein series attached to the modular group was proved by Luo and Sarnak, whereas a refined quantum variance formula and a strong mean value result was obtained recently by Huang. The Quantum unique ergodicity conjecture for degenerate Eisenstein series on \(\mathrm{GL}(n)\) was proved by L. Zhang in his PhD thesis. In our recent joint work with Corentin Darreye and Ikuya Kaneko we prove a quantum variance formula for \(\mathrm{GL}(n)\) degenerate Eisenstein series, as well as a stronger mean value result which goes beyond the Generalized Lindelöf Hypothesis.