We study the asymptotics of fundamental solutions of p-adic pseudodifferential equations of type (f(∂, β) + λ)u = g, where f(∂, β) is a pseudo-differential operator with symbol |f | K , β > 0, f is a form of arbitrary degree with coefficients in a p−adic field, λ ≥ 0, and g is a Schwartz-Bruhat function.

A new term in the p-adic world-sheet action is proposed, which couples a constant B-field to the boundary of the world-sheet at disk level. The induced deformation of tachyon scattering amplitudes by star-products is derived. This is in agreement with the deformation of effective action postulated in recent investigations of noncommutative solitons in p-adic string theory.

Throughout this paper, let p be a fixed odd prime number. The symbol, Zp, Qp and Cp denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. Let N be the set of natural numbers and Z+ = N ∪ {0}. As well known definition, the p-adic absolute value is given by |x|p = p−r where x = p t s with (t, p) = (s, p) = (t, s) = 1. When one talk...

We classify the filtered modules with coefficients corresponding to two-dimensional potentially semi-stable p-adic representations of the Galois groups of p-adic fields under the assumptions that p is odd and the coefficients are large enough. Introduction Let p be an odd prime number, and let K be a p-adic field. The absolute Galois group of K is denoted by GK . By the fundamental theorem of C...

In this paper, we take some initial steps towards illuminating the (hypothetical) p-adic local Langlands functoriality principle relating Galois representations of a p-adic field L and admissible unitary Banach space representations of G(L) when G is a split reductive group over L. 2000 Mathematics Subject Classification: 11F80, 11S37, 22E50

This paper is an expanded version of my lecture delivered at the 97 Seattle summer research conference on finite fields. It gives a quick exposition of Dwork’s conjecture about p-adic meromorphic continuation of his unit root L-function arising from a family of algebraic varieties defined over a finite field of characteristic p. As a simple illustration, we discuss the classical example of the ...

We generalize the methods of Moy-Prasad, in order to define and study the genuine depth zero representations of some nonlinear covers of reductive groups over p-adic local fields. In particular, we construct all depth zero supercuspidal representations of the metaplectic group Mp2n over a p-adic field of odd residue characteristic.