Displaying similar documents to “Абелевы группы с одним τ -aдическим соотношением”

On the heights of totally p -adic numbers

Paul Fili (2014)

Journal de Théorie des Nombres de Bordeaux


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


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


Let f ( z ) = z d + a d - 1 z d - 1 + . . . + a 1 z 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


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...

The geometry of non-unit Pisot substitutions

Milton Minervino, Jörg Thuswaldner (2014)

Annales de l’institut Fourier


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 Q ¯ ˜ p

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

Open Mathematics


Let p be a prime number, and let [...] Q¯ p 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 Q ¯ ˜ 𝐩 , the completion of Q with respect w, i.e. the spectral extension of the p-adic valuation vp on Q.

The Heyde theorem on a-adic solenoids

Margaryta Myronyuk (2013)

Colloquium Mathematicae


We prove the following analogue of the Heyde theorem for a-adic solenoids. Let ξ₁, ξ₂ be independent random variables with values in an a-adic solenoid Σ a and with distributions μ₁, μ₂. Let α j , β j be topological automorphisms of Σ a such that β α - 1 ± β α - 1 are topological automorphisms of Σ a too. Assuming that the conditional distribution of the linear form L₂ = β₁ξ₁ + β₂ξ₂ given L₁ = α₁ξ₁ + α₂ξ₂ is symmetric, we describe the possible distributions μ₁, μ₂.