Value distribution for eigenfunctions of desymmetrized quantum maps (Q2764645)

The paper is devoted to one aspect of the behaviour of eigenfunctions of classically chaotic quantum systems, namely their value distribution and specifically their extreme values. In the paper, this problem is studied for one of the well-known models in quantum chaotic dynamics - the quantized cat map (see \textit{J. H. Hannay} and \textit{M. V. Berry} [Phys. D 1, 267-290 (1980)]). NEWLINENEWLINENEWLINEThe paper is a continuation of the previous study \textit{P. Kurlberg} and \textit{Z. Rudnick} [Duke Math. J. 103, 47-77 (2000; Zbl 1013.81017)] where Hecke operators and Hecke eigenfunctions had been introduced, in analogy with the classical theory of modular forms, and it was shown that the Hecke eigenfunctions become uniformly distributed in the semiclassical limit. In the paper, suprema and value distributions of the Hecke eigenfunctions are investigated. The modern theory of exponential sums is used.