To a polynomial f over a non-archimedean local field K and a character Ï‡ of the group of units of the valuation ring of K one associates Igusa's local zeta function Z(s, f, Ï‡). In this paper, weâ€¦ (More)

In this paper we construct and study a fundamental solution of Cauchyâ€™s problem for pâˆ’adic parabolic equations of the type âˆ‚u (x, t) âˆ‚t + (f (D, Î²)u) (x, t) = 0, x âˆˆ Qnp , n â‰¥ 1, t âˆˆ (0, T ] , whereâ€¦ (More)

In this paper we provide a geometric description of the possible poles of the Igusa local zeta function Z (s; f) associated to an analytic mapping f = (f1; : : : ; fl) : U( Kn) ! Kl, and a locallyâ€¦ (More)

In this paper, we prove the rationality of Igusaâ€™s local zeta functions of semiquasihomogeneous polynomials with coefficients in a non-archimedean local field K. The proof of this result is based onâ€¦ (More)

We study the asymptotics of fundamental solutions of p-adic pseudodifferential equations of type (f(âˆ‚, Î²) + Î») u = g, where f(âˆ‚, Î²) is a pseudo-differential operator with symbol |f | K , Î² > 0, f isâ€¦ (More)

Abstract. Let K be a pâˆ’adic field, and ZÎ¦(s, f), s âˆˆ C, with Re(s) > 0, the Igusa local zeta function associated to f(x) = (f1(x), .., fl(x)) âˆˆ [K (x1, .., xn)] , and Î¦ a Schwartz-Bruhat function.â€¦ (More)

We give a polynomial time algorithm for computing the Igusa local zeta function Z(s, f) attached to a polynomial f(x) âˆˆ Z[x], in one variable, with splitting field Q, and a prime number p. We alsoâ€¦ (More)

This paper is dedicated to a description of the poles of the Igusa local zeta function Z(s, f, v) when f(x, y) satisfies a new non-degeneracy condition called arithmetic non-degeneracy. Moreâ€¦ (More)

We show that the solutions of pâˆ’adic pseudo-differential equations of wave type have a decay similar to the solutions of classical generalized wave equations.