On montre sous quelles conditions un élément analytique -adique peut être décomposé sous forme d’un produit de facteurs dont chacun est un élément analytique dans le complémentaire d’un disque.
Special values of certain functions of the type are studied where is a motive over a totally real field with coefficients in another field , andis an Euler product running through maximal ideals of the maximal order of andbeing a polynomial with coefficients in . Using the Newton and the Hodge polygons of one formulate a conjectural criterium for the existence of a -adic analytic continuation of the special values. This conjecture is verified in a number of cases related to...
AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75We perform analysis of certain aspects of approximation in multiplicative systems that appear as duals of ultrametric structures, e.g. in cases of local fields, totally disconnected Abelian groups satisfying the second axiom of countability or more general ultrametric spaces that do not necessarily possess a group structure. Using the fact that the unit sphere of a local field is a Vilenkin group, we introduce a new concept of differentiation in...