Noncommutative Geometry and Quantum Physics Vietri sul Mare, August 31 - September 5, 2009
Home page Speakers Participants Program Picture Lodging Travel Equipment Registration Sponsors	Speaker: Florin Radulescu, Rome Title: Quantum dynamics and the Ramanujan-Peterson conjecture Abstract: We prove that classical Hecke operators on Maass forms are a special case of completely positive maps on II1 factors, associated to a pair of isomorphic subfactors. This representation induces several matrix inequalities on the eigenvalues of the Hecke operators Maass forms. In particular the family of eigenvalues corresponding to an eigenvector is a completely bounded multiplier of the Hecke algebra. Moreover it follows that the Ramanujan-Peterson conjecture holds true, with the possible exception of a finite number of eigenvectors.
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