Igusa’s p-adic local zeta function associated to a polynomial mapping and a polynomial integration measure

A p-adic algorithm to compute the Hilbert class polynomial

Classicaly, the Hilbert class polynomial P∆ ∈ Z[X] of an imaginary quadratic discriminant ∆ is computed using complex analytic techniques. In 2002, Couveignes and Henocq [5] suggested a p-adic algorithm to compute P∆. Unlike the complex analytic method, it does not suffer from problems caused by rounding errors. In this paper we complete the outline given in [5] and we prove that, if the Genera...

p-ADIC LOGARITHMS FOR POLYNOMIAL DYNAMICS

We prove a dynamical version of the Mordell-Lang conjecture for subvarieties of the affine space A over a p-adic field, endowed with polynomial actions on each coordinate of A. We use analytic methods similar to the ones employed by Skolem, Chabauty, and Coleman for studying diophantine equations.

The Probability That a Random Monic p-adic Polynomial Splits

Uniform p-adic cell decomposition and local zeta functions

The purpose of this paper is to give a cell decomposition for p-adic fields, uniform in p. This generalizes a cell decomposition for fixed p, proved by Denef [7], [9]. We also give some applications of our cell decomposition. A first implication is a uniform quantifier elimination for p-adic fields. Beiair [2], Delon [6] and Weispfenning [16] obtained quantifier elimination in other languages, ...

Local Polynomial Variance Function Estimation

The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focussed on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The eeect of preliminary estimation of the mean is studied, and a \degrees of freedom"...