Related papers: Power series and p-adic algebraic closures

A general integral expression to transform power series is applied to $\arcsin{x}$ and its positive integer powers. We concentrate on the first to the fourth powers and obtain infinite classes of new power series involving central binomial…

We prove that dagger closure is trivial in regular domains containing a field and that graded dagger closure is trivial in polynomial rings over a field. We also prove that Heitmann's full rank one closure coincides with tight closure in…

We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p>2. A superalgebra generalization of the celebrated Kac-Weisfeiler Conjecture is formulated, which exhibits a…

We give bounds for the number and the size of the primes $p$ such that a reduction modulo $p$ of a system of multivariate polynomials over the integers with a finite number $T$ of complex zeros, does not have exactly $T$ zeros over the…

In previous papers, there were computed the Poincare series of some (multi-index) filtrations on the ring of germs of functions on a rational surface singularity. These Poincare series were written as the integer parts of certain fractional…

In this article, we study several probabilistic properties of polynomials defined over the ring of $p$-adic integers under the Haar measure. First, we calculate the probability that a monic polynomial is separable, generalizing a result of…

Let $k$ be a perfect field of characteristic $p > 2$. We extend the equivalence of categories between Fontaine-Laffaille modules and $\mathbb{Z}_p$ lattices inside crystalline representations with Hodge-Tate weights at most $p-2$ of…

Using the theory of pro-p groups and relative Poincar\'{e} duality, we define a type of cobordism category well suited to arithmetic topology. We completely classify topological quantum field theories on these two-dimensional versions of…

We consider formal power series in several variables with coefficients in arbitrary field such that their Newton polyhedron has a loose edge. We show that if the symbolic restriction of the power series $f$ to such an edge is a product of…

We prove an irreducibility criterion for polynomials with power series coefficients generalizing previous known results concerning quasi-ordinary polynomials.

This study is devoted to the polynomial representation of the matrix $p$th root functions. The Fibonacci-H\"orner decomposition of the matrix powers and some techniques arisen from properties of generalized Fibonacci sequences, notably the…

The Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial $p$ of degree $d$ as a finite sum of $d$-{th} powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any…

We consider summation of some finite and infinite functional p-adic series with factorials. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer…

We show that the coefficients of a power series occurring in $p$-adic Fourier theory for $\mathbf{Q}_{p^2}$ have valuations that are given by an intriguing formula.

The algebraic properties of formal power series, whose coefficients show factorial growth and admit a certain well-behaved asymptotic expansion, are discussed. It is shown that these series form a subring of $\mathbb{R}[[x]]$. This subring…

Being closed under truncation for subsets of generalized series fields is a robust property in the sense that it is preserved under various algebraic and transcendental extension procedures. Nevertheless, in Chapter 4 of this dissertation,…

We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.

We prove that the integral closure of a Poisson algebra $A$ over a field of characteristic 0 is again a Poisson algebra.

The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…

In this note we extend some of the results of a previous paper \url{arXiv:math/0511593} to algebraically closed fields of finite characteristic. In particular, we show that there is an explicit expression in $n$ and $d$ which is divisible…