Displaying similar documents to “Indecomposable Z p [ G ] -lattices for a class of metabelian groups”

On a generalization of Craig lattices

Hao Chen (2013)

Journal de Théorie des Nombres de Bordeaux

Similarity:

In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range 3332 - 4096 which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range 128 - 3272 . We also construct some dense lattices of dimensions in the range 4098 - 8232 . Finally we also obtain some new lattices of moderate dimensions such as 68 , 84 , 85 , 86 , which are denser...

The geometry of non-unit Pisot substitutions

Milton Minervino, Jörg Thuswaldner (2014)

Annales de l’institut Fourier

Similarity:

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 heights of totally p -adic numbers

Paul Fili (2014)

Journal de Théorie des Nombres de Bordeaux

Similarity:

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

Similarity:

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...

The Heyde theorem on a-adic solenoids

Margaryta Myronyuk (2013)

Colloquium Mathematicae

Similarity:

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 ₁ α - 1 ₁ ± β ₂ α - 1 ₂ 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.

Base change for Bernstein centers of depth zero principal series blocks

Thomas J. Haines (2012)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Let  G be an unramified group over a p -adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for  G and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with Γ 1 ( p ) -level structure initiated by M. Rapoport and the author in [15].

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

G. Gát (2001)

Studia Mathematica

Similarity:

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...

A note on p-adic valuations of Schenker sums

Piotr Miska (2015)

Colloquium Mathematicae

Similarity:

A prime number p is called a Schenker prime if there exists n ∈ ℕ₊ such that p∤n and p|aₙ, where a ₙ = ∑ j = 0 n ( n ! / j ! ) n j is a so-called Schenker sum. T. Amdeberhan, D. Callan and V. Moll formulated two conjectures concerning p-adic valuations of aₙ when p is a Schenker prime. In particular, they conjectured that for each k ∈ ℕ₊ there exists a unique positive integer n k < 5 k such that v ₅ ( a m · 5 k + n k ) ≥ k for each nonnegative integer m. We prove that for every k ∈ ℕ₊ the inequality v₅(aₙ) ≥ k has exactly one solution modulo 5 k . This...

On the closed subfields of [...] Q ¯   p Q ¯ ˜ p

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

Open Mathematics

Similarity:

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.

Counting arithmetic subgroups and subgroup growth of virtually free groups

Amichai Eisenmann (2015)

Journal of the European Mathematical Society

Similarity:

Let K be a p -adic field, and let H = P S L 2 ( K ) endowed with the Haar measure determined by giving a maximal compact subgroup measure 1 . Let A L H ( x ) denote the number of conjugacy classes of arithmetic lattices in H with co-volume bounded by x . We show that under the assumption that K does not contain the element ζ + ζ - 1 , where ζ denotes the p -th root of unity over ℚ p , we have lim x → ∞ log A L H ( x ) x log x = q - 1 where q denotes the order of the residue field of K .

Overconvergent modular symbols and p -adic L -functions

Robert Pollack, Glenn Stevens (2011)

Annales scientifiques de l'École Normale Supérieure

Similarity:

This paper is a constructive investigation of the relationship between classical modular symbols and overconvergent p -adic modular symbols. Specifically, we give a constructive proof of a (Theorem 1.1) due to the second author [19] proving existence and uniqueness of overconvergent eigenliftings of classical modular eigensymbols of . As an application we describe a polynomial-time algorithm for explicit computation of associated p -adic L -functions in this case. In the case of, the control...

On non-basic Rapoport-Zink spaces

Elena Mantovan (2008)

Annales scientifiques de l'École Normale Supérieure

Similarity:

In this paper we study certain moduli spaces of Barsotti-Tate groups constructed by Rapoport and Zink as local analogues of Shimura varieties. More precisely, given an isogeny class of Barsotti-Tate groups with unramified additional structures, we investigate how the associated (non-basic) moduli spaces compare to the (basic) moduli spaces associated with its isoclinic constituents. This aspect of the geometry of the Rapoport-Zink spaces is closely related to Kottwitz’s prediction that...