Neural multigrid for gauge theories and other disordered systems

We present evidence that multigrid works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder, but one needs to introduce a "neural computations" point of view into large scale simulations: First, the system must learn how to do the simulations efficiently, then do the simulation (fast). The method can also be used to provide smooth interpolation kernels which are needed in multigrid Monte Carlo updates.Comment: 9 pages [2 figures appended in PostScript format], preprint DESY 92-126, Sept. 199

On the Eisenstein cohomology of odd orthogonal groups

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes for maximal parabolic Q-subgroups in case of generic cohomological cuspidal automorphic representations of their Levi subgroups. That is, such identifying necessary conditions on these latter representations as well as on the complex parameters in order for the associated Eisenstein series to possibly yield non-trivial classes in the automorphic cohomology.Comment: 21 pages, some minor corrections made, journal reference adde

Asymptotics of class numbers

A "simple trace formula" is used to derive an asymptotic result for class numbers of complex cubic orders.Comment: 37 page