%0 Journal Article
%T On Baxter Q-operators And Their Arithmetic Implications
%A A. Gerasimov
%A D. Lebedev
%A S. Oblezin
%J Mathematics
%D 2007
%I arXiv
%X We consider Baxter Q-operators for various versions of quantum affine Toda chain. The interpretation of eigenvalues of the finite Toda chain Baxter operators as local Archimedean L-functions proposed recently is generalized to the case of affine Lie algebras. We also introduce a simple generalization of Baxter operators and local L-functions compatible with this identification. This gives a connection of the Toda chain Baxter Q-operators with an Archimedean version of the Polya-Hilbert operator proposed by Berry-Kitting. We also elucidate the Dorey-Tateo spectral interpretation of eigenvalues of Q-operators. Using explicit expressions for eigenfunctions of affine/relativistic Toda chain we obtain an Archimedean analog of Casselman-Shalika-Shintani formula for Whittaker function in terms of characters.
%U http://arxiv.org/abs/0711.2812v2