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Journals and Conferences
To a polynomial f over a non-archimedean local field K and a character χ of the group of units of the valuation ring of K one associates Igusa's local zeta function Z(s, f, χ). In this paper, we… (More)
In this paper we construct and study a fundamental solution of Cauchy’s problem for p−adic parabolic equations of the type ∂u (x, t) ∂t + (f (D, β)u) (x, t) = 0, x ∈ Qnp , n ≥ 1, t ∈ (0, T ] , where… (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 locally… (More)
In this paper, we prove the rationality of Igusa’s local zeta functions of semiquasihomogeneous polynomials with coefficients in a non-archimedean local field K. The proof of this result is based on… (More)
We show the existence of fundamental solutions for p−adic pseudo-differential operators with polynomial symbols.
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… (More)
Abstract. Let K be a p−adic field, and ZΦ(s, f), s ∈ C, with Re(s) > 0, the Igusa local zeta function associated to f(x) = (f1(x), .., fl(x)) ∈ [K (x1, .., xn)] , and Φ a Schwartz-Bruhat function.… (More)
We give a polynomial time algorithm for computing the Igusa local zeta function Z(s, f) attached to a polynomial f(x) ∈ Z[x], in one variable, with splitting field Q, and a prime number p. We also… (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. More… (More)
We show that the solutions of p−adic pseudo-differential equations of wave type have a decay similar to the solutions of classical generalized wave equations.