Commutative algebraic groups and p-adic linear forms

Clemens Fuchs; Duc Hiep Pham

Displaying similar documents to “Commutative algebraic groups and p-adic linear forms”

On the heights of totally $p$ -adic numbers

Paul Fili (2014)

Journal de Théorie des Nombres de Bordeaux

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Bombieri and Zannier established lower and upper bounds for the limit infimum of the Weil height in fields of totally $p$ -adic numbers and generalizations thereof. In this paper, we use potential theoretic techniques to generalize the upper bounds from their paper and, under the assumption of integrality, to improve slightly upon their bounds.

Heights and totally p-adic numbers

Lukas Pottmeyer (2015)

Acta Arithmetica

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We study the behavior of canonical height functions $h ̂_{f}$ , associated to rational maps f, on totally p-adic fields. In particular, we prove that there is a gap between zero and the next smallest value of $h ̂_{f}$ on the maximal totally p-adic field if the map f has at least one periodic point not contained in this field. As an application we prove that there is no infinite subset X in the compositum of all number fields of degree at most d such that f(X) = X for some non-linear polynomial f. This...

Bounds on the radius of the p-adic Mandelbrot set

Jacqueline Anderson (2013)

Acta Arithmetica

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Let $f (z) = z^{d} + a_{d - 1} z^{d - 1} + . . . + a_{1} z \in ℂ_{p} [z]$ be a degree d polynomial. We say f is post-critically bounded, or PCB, if all of its critical points have bounded orbit under iteration of f. It is known that if p ≥ d and f is PCB, then all critical points of f have p-adic absolute value less than or equal to 1. We give a similar result for 1/2d ≤ p < d. We also explore a one-parameter family of cubic polynomials over ℚ₂ to illustrate that the p-adic Mandelbrot set can be quite complicated when p < d, in contrast with the...

On (C,1) summability for Vilenkin-like systems

G. Gát (2001)

Studia Mathematica

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We give a common generalization of the Walsh system, Vilenkin system, the character system of the group of 2-adic (m-adic) integers, the product system of normalized coordinate functions for continuous irreducible unitary representations of the coordinate groups of noncommutative Vilenkin groups, the UDMD product systems (defined by F. Schipp) and some other systems. We prove that for integrable functions σₙf → f (n → ∞) a.e., where σₙf is the nth (C,1) mean of f. (For the character...

Абелевы группы с одним $τ$ -aдическим соотношением

A.A. Фомин (1989)

Algebra i Logika

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Indecomposable $Z_{p} [G]$ -lattices for a class of metabelian groups

R. Marszałek (1990)

Colloquium Mathematicae

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On the quasi-periodic $p$ -adic Ruban continued fractions

Basma Ammous, Nour Ben Mahmoud, Mohamed Hbaib (2022)

Czechoslovak Mathematical Journal

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We study a family of quasi periodic $p$ -adic Ruban continued fractions in the $p$ -adic field $ℚ_{p}$ and we give a criterion of a quadratic or transcendental $p$ -adic number which based on the $p$ -adic version of the subspace theorem due to Schlickewei.

The cubics which are differences of two conjugates of an algebraic integer

Toufik Zaimi (2005)

Journal de Théorie des Nombres de Bordeaux

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We show that a cubic algebraic integer over a number field $K,$ with zero trace is a difference of two conjugates over $K$ of an algebraic integer. We also prove that if $N$ is a normal cubic extension of the field of rational numbers, then every integer of $N$ with zero trace is a difference of two conjugates of an integer of $N$ if and only if the $3 -$ adic valuation of the discriminant of $N$ is not $4 .$

The geometry of non-unit Pisot substitutions

Milton Minervino, Jörg Thuswaldner (2014)

Annales de l’institut Fourier

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It is known that with a non-unit Pisot substitution $σ$ one can associate certain fractal tiles, so-called Rauzy fractals. In our setting, these fractals are subsets of a certain open subring of the adèle ring of the associated Pisot number field. We present several approaches on how to define Rauzy fractals and discuss the relations between them. In particular, we consider Rauzy fractals as the natural geometric objects of certain numeration systems, in terms of the dual of the one-dimensional...

On the closed subfields of [...] Q ¯ p ${\tilde{\bar{Q}}}_{p}$

Sever Achimescu, Victor Alexandru, Corneliu Stelian Andronescu (2016)

Open Mathematics

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Let p be a prime number, and let [...] Q¯ p ${\tilde{\bar{Q}}}_{𝐩}$ be the completion of Q with respect to the pseudovaluation w which extends the p-adic valuation vp. In this paper our goal is to give a characterization of closed subfields of [...] Q¯ p ${\tilde{\bar{Q}}}_{𝐩}$ , the completion of Q with respect w, i.e. the spectral extension of the p-adic valuation vp on Q.

On a noncommutative Iwasawa main conjecture for varieties over finite fields

Malte Witte (2014)

Journal of the European Mathematical Society

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We formulate and prove an analogue of the noncommutative Iwasawa main conjecture for $ℓ$ -adic Lie extensions of a separated scheme $X$ of finite type over a finite field of characteristic prime to $ℓ$ .

On Morita’s $p$ -adic $Γ$ -function

Daniel Baesky (1977-1978)

Groupe de travail d'analyse ultramétrique

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