Monday March 4, 2001

Speaker: Laurent Berger

Title: Approximation by polynomials with integral coefficients

Abstract: If K is a compact subset of the real numbers R, then a theorem of Weierstrass says that every continuous function f : K -> R is a uniform limit of polynomials. But which functions are limits of polynomials with integral coefficients? For example, if 0 is in K, then f(0) must be an integer. We will see that the general answer depends on arithmetical and geometric properties of K.