Indagationes Mathematicae-New Series最新文献

英文中文

A characterization of differential operators in the ring of complex polynomials 复多项式环中微分算子的表征

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2024-11-01 DOI: 10.1016/j.indag.2024.07.011

Włodzimierz Fechner , Eszter Gselmann

The paper aims to provide a full characterization of all operators

T : P (ℂ) \to P (ℂ)

acting on the space of all complex polynomials that satisfy the Leibniz rule

T (f \cdot g) = T (f) \cdot g + f \cdot T (g)

for all

f, g \in P (ℂ)

. We do not assume the linearity of

T

. As we will see, contrary to the well-known theorems for function spaces there are many other solutions here, not only differential operators. From our main result, we also derive two corollaries, showing that in some special cases operators that satisfy the Leibniz rule have some particular form.

本文旨在提供作用于所有复多项式空间的算子 T:P(ℂ)→P(ℂ) 的所有算子的完整特征，对于所有 f，g∈P(ℂ)，这些算子满足莱布尼兹规则 T(f⋅g)=T(f)⋅g+f⋅T(g) 。我们将看到，与众所周知的函数空间定理相反，这里不仅有微分算子，还有许多其他解。根据我们的主要结果，我们还推导出两个推论，说明在某些特殊情况下，满足莱布尼兹规则的算子具有某种特殊形式。

引用次数: 0

Finite odometer factors of rank one group actions 一级群作用的有限里程表因子

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2024-11-01 DOI: 10.1016/j.indag.2024.04.012

In this paper, we give explicit conditions characterizing the Følner rank one group actions that factor onto a finite odometer; those that factor onto an arbitrary, but specified odometer, and those that factor onto an unspecified odometer. We also give explicit conditions describing the Følner rank one actions that are conjugate to a specific odometer, and those that are conjugate to some odometer. These conditions are based on cutting and stacking procedures used to generate the action, and generalize results given by Foreman, Gao, Hill, Silva and Weiss for rank one

Z

-actions.

在本文中，我们给出了明确的条件，描述了因数为有限里程表的福尔纳一级群作用、因数为任意但指定里程表的群作用以及因数为未指定里程表的群作用。我们还给出了明确的条件，描述了与特定里程表共轭的福尔纳等级一动作，以及与某些里程表共轭的福尔纳等级一动作。这些条件基于生成作用的切割和堆叠程序，并概括了福尔曼、高、希尔、席尔瓦和韦斯给出的秩一 Z 作用的结果。

引用次数: 0

A note on the inverse problem for finite differential Galois groups 关于有限微分伽罗瓦群逆问题的说明

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2024-11-01 DOI: 10.1016/j.indag.2024.06.005

In this paper we revisit the following inverse problem: given a curve invariant under an irreducible finite linear algebraic group, can we construct an ordinary linear differential equation whose Schwarz map parametrizes it? We present an algorithmic solution to this problem under the assumption that we are given the function field of the quotient curve. The result provides a generalization and an efficient implementation of the solution to the inverse problem exposed by van der Put et al. (2020). As an application, we show that there is no hypergeometric equation with projective differential Galois group isomorphic to

H_{72}

, thus completing Beukers and Heckman’s answer (Beukers and Heckman, 1989) to the question of which irreducible finite subgroup of

P S L_{3} (ℂ)

are the projective monodromy of a hypergeometric equation.

在本文中，我们重新探讨了以下反向问题：给定一条在不可还原有限线性代数群下不变的曲线，我们能否构造一个其施瓦茨映射参数化的常线性微分方程？我们假设给定了商曲线的函数域，从而提出了这一问题的算法解决方案。这一结果提供了 van der Put 等人（2020 年）所揭示的逆问题解决方案的一般化和高效实现。作为应用，我们证明了不存在投影微分伽罗瓦群与，同构的超几何方程，从而完成了 Beukers 和 Heckman 对哪个不可还原有限子群是超几何方程的投影单色性问题的解答（Beukers 和 Heckman，1989 年）。

引用次数: 0

An analogue of a conjecture of Rasmussen and Tamagawa for abelian varieties over function fields 拉斯穆森和玉川对函数域上无性变种猜想的类比

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2024-11-01 DOI: 10.1016/j.indag.2024.06.007

Mentzelos Melistas

Let

L

be a number field and let

ℓ

be a prime number. Rasmussen and Tamagawa conjectured, in a precise sense, that abelian varieties whose field of definition of the

ℓ

-power torsion is both a pro-

ℓ

extension of

L (μ_{ℓ})

and unramified away from

ℓ

are quite rare. In this paper, we formulate an analogue of the Rasmussen–Tamagawa conjecture for non-isotrivial abelian varieties defined over function fields. We provide a proof of our analogue in the case of elliptic curves. In higher dimensions, when the base field is a subfield of the complex numbers, we show that our conjecture is a consequence of the uniform geometric torsion conjecture. Finally, using a theorem of Bakker and Tsimerman we also prove our conjecture unconditionally for abelian varieties with real multiplication.

设 L 是一个数域，ℓ 是一个素数。Rasmussen 和 Tamagawa 在精确的意义上猜想，其 ℓ-power torsion 的定义域既是 L(μℓ) 的 pro-ℓ 扩展，又远离 ℓ 无ramified 的无方变体是非常罕见的。在本文中，我们针对定义在函数域上的非等边无性变体，提出了拉斯穆森-玉川猜想（Rasmussen-Tamagawa conjecture）的类比。我们提供了在椭圆曲线情况下的类比证明。在更高维度上，当基域是复数的子域时，我们证明了我们的猜想是均匀几何扭转猜想的结果。最后，我们还利用巴克尔和齐默尔曼的一个定理，无条件地证明了我们的猜想适用于具有实乘法的无方变体。

引用次数: 0

The Generalized Riemann Hypothesis from zeros of a single L-function 从单一 L 函数的零点出发的广义黎曼假说

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2024-11-01 DOI: 10.1016/j.indag.2024.07.009

William Banks

For each primitive Dirichlet character

χ

, a hypothesis

{GRH}^{†} [χ]

is formulated in terms of zeros of the associated

L

-function

L (s, χ)

. It is shown that for any such character,

{GRH}^{†} [χ]

is equivalent to the Generalized Riemann Hypothesis.

对于每个原始 Dirichlet 字符 χ，都会根据相关 L 函数 L(s,χ) 的零点提出一个假设 GRH†[χ]。结果表明，对于任何这样的特征，GRH†[χ] 都等价于广义黎曼假设。

引用次数: 0

Non-Hausdorff germinal groupoids for actions of countable groups 可数群作用的非豪斯多夫萌芽群形

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2024-11-01 DOI: 10.1016/j.indag.2024.05.005

We study conditions under which the germinal groupoid associated to a minimal equicontinuous action of a countable group on a Cantor set has non-Hausdorff topology. We develop a new criterion, which serves as an obstruction for the étale topology on the groupoid to be non-Hausdorff. We use this and other criteria to study the topology of germinal groupoids for a few classes of actions. In particular, we give examples of families of contracting and non-contracting self-similar groups, which are amenable and whose actions have associated germinal groupoids with non-Hausdorff topology.

我们研究了与康托集上可数群的最小等连续作用相关联的萌芽群具有非豪斯多夫拓扑的条件。我们提出了一个新标准，该标准阻碍了群上的埃塔拓扑为非豪斯多夫拓扑。我们利用这个标准和其他标准研究了几类作用的胚芽群拓扑学。特别是，我们举例说明了收缩和非收缩自相似群的家族，这些家族是可和的，其作用具有相关的非豪斯多夫拓扑的萌芽群。

引用次数: 0

Critical curves of rotations 旋转的临界曲线

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2024-09-01 DOI: 10.1016/j.indag.2024.02.001

In rotations with a binary symbolic dynamics, a critical curve is the locus of parameters for which the boundaries of the partition that defines the symbolic dynamics are connected via a prescribed number of iterations and symbolic itinerary. We study the arithmetical and geometrical properties of these curves in parameter space.

在具有二元符号动力学的旋转中，临界曲线是参数的位置，在该位置上，定义符号动力学的分区边界通过规定的迭代次数和符号行程相连。我们研究了这些曲线在参数空间中的算术和几何特性。

引用次数: 0

Semicocycle discontinuities for substitutions and reverse-reading automata 替换和反读自动机的半循环不连续

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2024-09-01 DOI: 10.1016/j.indag.2023.05.003

In this article we define the semigroup associated to a primitive substitution. We use it to construct a minimal automaton which generates a substitution sequence $u$ in reverse reading. We show, in the case where the substitution has a coincidence, that this automaton completely describes the semicocycle discontinuities of $u$ .

在本文中，我们定义了与原始替换相关的半群。我们用它来构造一个最小自动机，以反向阅读的方式生成一个替换序列 u。我们证明，在替换具有重合性的情况下，这种自动机可以完全描述 u 的半周期不连续性。

引用次数: 0

Automorphism groups of random substitution subshifts 随机替换子移的自同构群

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2024-09-01 DOI: 10.1016/j.indag.2023.08.006

We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are countable, non-amenable and non-residually finite. To show this, we introduce the concept of shuffles and generalised shuffles for random substitutions, as well as a local version of recognisability for random substitutions that will be of independent interest. Without recognisability, we need a more refined notion of recognisable words in order to understand their automorphisms. We show that the existence of a single recognisable word is often enough to embed the automorphism group of a full shift in the automorphism group of the random substitution subshift.

我们证明，对于一类合适的随机置换，其相应的子移位的自变群包含一个无限简单子群和一个全移位自变群的副本。因此，它们是可数的、不可门的和非剩余有限的。为了证明这一点，我们引入了随机置换的洗牌和广义洗牌的概念，以及随机置换的可识别性的局部版本。如果没有可识别性，我们就需要一个更精细的可识别词概念，以便理解它们的自动变形。我们证明，一个可识别词的存在往往足以将全移位的自形群嵌入随机置换子移位的自形群中。

引用次数: 0

Inter-model sets in Rd are model sets Rd中的模型间集是模型集

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2024-09-01 DOI: 10.1016/j.indag.2023.06.007

We show that any union of finitely many shifted model sets from a given cut-and-project scheme is a model set in some modified cut-and-project scheme. Restricting to direct space $R^{d}$ , we show that any inter-model set is a model set in some modified cut-and-project scheme with second countable internal space. In both cases, the window in the modified cut-and-project scheme inherits the topological and measure-theoretic properties of the original windows.

我们证明，给定切分方案中有限多个移位模型集的任何联合都是某个修正切分方案中的模型集。限于直接空间 Rd，我们证明任何模型间集合都是某个具有第二可数内部空间的修正切分方案中的模型集合。在这两种情况下，修正的切分-投影方案中的窗口都继承了原始窗口的拓扑和度量理论性质。

引用次数: 0

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