Bounds on supremum norms for Hecke eigenfunctions of quantized cat maps
2007 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 8, no 1, 75-89 p.Article in journal (Refereed) Published
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 <<(epsilon) N-epsilon for all epsilon > 0 in the case of N square free.
Place, publisher, year, edition, pages
2007. Vol. 8, no 1, 75-89 p.
riemannian-manifolds, toral automorphisms, quantum, equidistribution, surfaces, torus
IdentifiersURN: urn:nbn:se:kth:diva-16409DOI: 10.1007/s00023-006-0300-xISI: 000244446900004ScopusID: 2-s2.0-33847276752OAI: oai:DiVA.org:kth-16409DiVA: diva2:334451
QC 201005252010-08-052010-08-05Bibliographically approved