The Index of Stickelberger Ideals of Order2 and Cuspidal Class Numbers .
We study the infinitesimal generator of the Lax-Phillips semigroup of the automorphic scattering system defined on the Poincaré upper half-plane for SL₂(ℤ). We show that its spectrum consists only of the poles of the resolvent of the generator, and coincides with the poles of the scattering matrix, counted with multiplicities. Using this we construct an operator whose eigenvalues, counted with algebraic multiplicities (i.e. dimensions of generalized eigenspaces), are precisely the non-trivial zeros...
Let be a locally compact non-Archimedean field, and let be a division algebra of dimension 4. The Jacquet-Langlands correspondence provides a bijection between smooth irreducible representations of of dimension and irreducible cuspidal representations of . We present a new construction of this bijection in which the preservation of epsilon factors is automatic. This is done by constructing a family of pairs , where is an order and is a finite-dimensional representation of a certain...