Holomorphic Hecke Cusp Forms and Quantum Chaos

Abstract: Arithmetic Quantum Chaos (AQC) is an active area of research at the intersection of number theory and physics. One major goal in AQC is to study the mass distribution and behaviour of Hecke Maass cusp forms on hyperbolic surfaces as the Laplace eigenvalue tends to infinity. In this talk we will focus on analogous questions for holomorphic Hecke cusp forms. First, we will review some of the important solved and unsolved questions in the area, like the Quantum Unique Ergodicity problem or the Gaussian Moment Conjecture. We then elaborate on a sharp bound for the fourth moment of holomorphic cusp forms and ongoing work on evaluating the averaged sixth moment of holomorphic cusp forms. These are special instances of the Gaussian Moment Conjecture.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html