An Isaac Newton Institute Workshop

Random Matrix Theory and Arithmetic Aspects of Quantum Chaos

On the Remainder in Weyl's Law for Heisenberg Manifolds

Author: Yiannis Petridis (City University of New York, Lehman College)

Abstract

We examine the error term in Weyl's law for the distribution of Laplace eigenvalues for Heisenberg manifolds equipped with a left-invariant metric. We formulate conjectures on the optimal size and evidence for the conjectures. We explain the analogies with the classical Dirichlet divisor problem in analytic number theory. This program has been developped jointly with D. Chung, M. Khosravi and J. Toth.

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