Bounds on Supremum Norms for Hecke Eigenfunctions of Quantized Cat Maps |
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Authors: | Pär Kurlberg |
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Institution: | (1) Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden |
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Abstract: | We study extreme values of desymmetrized eigenfunctions (so called Hecke eigenfunctions) for the quantized cat map, a quantization
of a hyperbolic linear map of the torus. In a previous paper it was shown that for prime values of the inverse Planck’s constant
N = 1/h, such that the map is diagonalizable (but not upper triangular) modulo N, the Hecke eigenfunctions are uniformly bounded. The purpose of this paper is to show that the same holds for any prime N provided that the map is not upper triangular modulo N. We also find that the supremum norms of Hecke eigenfunctions are ≪ε Nε for all ε > 0 in the case of N square free.
Submitted: March 6, 2006; Accepted: April 30, 2006 |
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