Heisenberg Realizations, Eigenfunctions and Proof of the Kurlberg-Rudnick Supremum Conjecture

Abstract

In this paper, proof of the {\it Kurlberg-Rudnick supremum conjecture} for the quantum Hannay-Berry model is presented. This conjecture was stated in P. Kurlberg's lectures at Bologna 2001 and Tel-Aviv 2003. The proof is a primer application of a fundamental solution: all the Hecke eigenfunctions of the quantum system are constructed. The main tool in our construction is the categorification of the compatible system of realizations of the Heisenberg representation over a finite field. This enables us to construct certain "perverse sheaves" that stands motivically prior to the Hecke eigenfunctions.

Preliminary version, 31 pages

References in corpus (1)

• Kazhdan-Laumon representations of finite Chevalley groups, character sheaves and some generalization of the Lefschetz-Verdeier trace formula

Cited by in corpus (4)

• Bounds on supremum norms for Hecke eigenfunctions of quantized cat maps
• On matrix elements for the quantized cat map modulo prime powers
• Bounds on certain Higher-Dimensional Exponential Sums via the Self-Reducibility of the Weil Representation
• Notes on quantization of symplectic vector spaces over finite fields