Periodicity in the p-adic valuation of a polynomial

The 2-adic Valuation of the Coefficients of a Polynomial

from which it follows that dl(m) is a rational number with only a power of 2 in its denominator. Extensive calculations have shown that, with rare exceptions, the numerators of dl(m) contain a single large prime divisor and its remaining factors are very small. For example d6(30) = 2 12 · 7 · 11 · 13 · 17 · 31 · 37 · 639324594880985776531. Similarly, d10(200) has 197 digits with a prime factor ...

THE p-ADIC VALUATION OF k-CENTRAL BINOMIAL COEFFICIENTS

The coefficients c(n, k) defined by (1− kx) = X n≥0 c(n, k)x reduce to the central binomial coefficients `

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

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...