Universal Laurent series on domains of infinite connectivity

Infinite transitivity on universal torsors

Let X be an algebraic variety covered by open charts isomorphic to the affine space and q : X̂ → X be the universal torsor over X . We prove that the automorphism group of the quasiaffine variety X̂ acts on X̂ infinitely transitively. Also we find wide classes of varieties X admitting such a covering.

Diagonalization and Rationalization of Algebraic Laurent Series

— We prove a quantitative version of a result of Furstenberg [20] and Deligne [13] stating that the the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime p the reduction modulo p of the diagonal of a multivariate algebraic power series f with integer coefficients is an algebrai...

Spectral Elements on Infinite Domains

AN INTRODUCTION TO THE THEORY OF DIFFERENTIABLE STRUCTURES ON INFINITE INTEGRAL DOMAINS

A special class of differentiable functions on an infinite integral domain which is not a field is introduced. Some facts about these functions are established and the special case of z is studied in more detail

Inverse polynomial expansions of Laurent series, II

An algorithm is considered, and shown to lead to various unusual and unique series expansions of formal Laurent series, as the sums of reciprocals of polynomials. The degrees of approximation by the rational functions which are the partial sums of these series are investigated. The types of series corresponding to rational functions themselves are also partially characterized.