Introduction. The purpose of this article is to introduce the general mathematical community to some recent developments in algebraic geometry and nonarchimedean analysis. Let r = p,p a rational prime. Then these developments center around the beginnings of an "arithmetic" theory of the polynomial ring ¥r[T] over the finite field of r elements. The goal of this theory is to use nonarchimedean a...

In this paper we study the automorphisms of Siegel upper half plane of complex dimension 3. We give the normal forms and classify the set of fixed points of such transformations. 1

The Coulomb-gas description of minimal models is considered on the half plane. Screening prescriptions are developed by the perturbative expansion of the Liouville theory with imaginary coupling and with Neumann boundary condition on the bosonic field. To generate the conformal blocks of more general boundary conditions, we propose the insertion of boundary operations.

We use the biorthogonal multiwavelets related by differentiation constructed in previous work to construct compactly supported biorthogonal multiwavelet bases for the space of vector fields on the upper half plane R+ such that the reconstruction wavelets are divergence-free and have vanishing normal components on the boundary of R+. Such wavelets are suitable to study the Navier–Stokes equation...