Expositiones Mathematicae最新文献

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A note on the standard zero-free region for L-functions 关于 L 函数标准无零区域的说明

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae

Pub Date : 2024-10-17 DOI: 10.1016/j.exmath.2024.125624

In this short note, we establish a standard zero-free region for a general class of

L

-functions for which their logarithms have coefficients with nonnegative real parts, including the Rankin–Selberg

L

-functions for unitary cuspidal automorphic representations.

在这篇短文中，我们为L函数对数具有非负实部系数的一类L函数建立了标准无零区域，其中包括单单元骤然自动表征的Rankin-Selberg L函数。

引用次数: 0

Brownian motion in a vector space over a local field is a scaling limit 局部场上矢量空间中的布朗运动是一种缩放极限

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae

Pub Date : 2024-09-27 DOI: 10.1016/j.exmath.2024.125607

For any natural number

d

, the Vladimirov–Taibleson operator is a natural analogue of the Laplace operator for complex-valued functions on a

d

-dimensional vector space

V

over a local field

K

. Just as the Laplace operator on

L^{2} (R^{d})

is the infinitesimal generator of Brownian motion with state space

R^{d}

, the Vladimirov–Taibleson operator on

L^{2} (V)

is the infinitesimal generator of real-time Brownian motion with state space

V

. This study deepens the formal analogy between the two types of diffusion processes by demonstrating that both are scaling limits of discrete-time random walks on a discrete group. It generalizes the earlier works, which restricted

V

to be the

p

-adic numbers.

对于任意自然数 d，弗拉基米洛夫-泰伯松算子是局部域 K 上 d 维向量空间 V 上复值函数拉普拉斯算子的自然类似物。正如 L2(Rd) 上的拉普拉斯算子是状态空间为 Rd 的布朗运动的无穷小发生器一样，L2(V) 上的 Vladimirov-Taibleson 算子是状态空间为 V 的实时布朗运动的无穷小发生器。本研究通过证明这两种扩散过程都是离散群上离散时间随机游走的缩放极限，深化了这两种扩散过程之间的形式类比。它概括了以前的研究，以前的研究把 V 限制为 p-adic 数。

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引用次数: 0

Abelian groups acting on the line 作用于直线的阿贝尔群

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae

Pub Date : 2024-09-26 DOI: 10.1016/j.exmath.2024.125619

We study the action of finitely generated Abelian subgroups of

H o m e o_{+} (R)

We propose a presentation where the focus is on understanding the set of stabilizers, which yields a dynamical description of the action that is both elementary and self-contained.

我们研究了 Homeo+(R)的有限生成阿贝尔子群的作用。我们提出了一种演示方法，其重点在于理解稳定子的集合，从而得到既基本又自足的作用的动力学描述。

引用次数: 0

Some useful tools in the study of nonlinear elliptic problems 研究非线性椭圆问题的一些有用工具

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae

Pub Date : 2024-09-16 DOI: 10.1016/j.exmath.2024.125616

This paper gives an overview of some basic aspects concerning the qualitative analysis of nonlinear, nonhomogeneous elliptic problems. We are concerned with two classes of elliptic equations with Dirichlet boundary condition. The first problem is driven by a general nonhomogeneous differential operator, which includes several usual operators (such as the $(p, q)$ -Laplace operator introduced by P. Marcellini). Next, we focus on differential operators with unbalanced growth in the nonautonomous case. Our analysis will point out some relevant differences between balanced and unbalanced growth problems. The presentation is done in the context of Dirichlet problems but a similar analysis can be developed for other boundary conditions, such as Neumann or Robin.

本文概述了非线性、非均质椭圆问题定性分析的一些基本方面。我们关注两类具有 Dirichlet 边界条件的椭圆方程。第一个问题由一般非均质微分算子驱动，其中包括几个常见算子（如 P. Marcellini 引入的 (p,q)-Laplace 算子）。接下来，我们将重点讨论非自治情况下不平衡增长的微分算子。我们的分析将指出平衡增长和非平衡增长问题之间的一些相关区别。我们以 Dirichlet 问题为背景进行介绍，但类似的分析也可用于其他边界条件，如 Neumann 或 Robin。

引用次数: 0

An introduction to pointwise sparse domination 点式稀疏支配导论

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae

Pub Date : 2024-09-04 DOI: 10.1016/j.exmath.2024.125605

The goal of this expository paper is to give a self-contained introduction to sparse domination. This is a method relying on techniques from dyadic Harmonic Analysis which has received a lot of attention in recent years. Essentially, it allows for a unified approach to proving weighted norm inequalities for a large variety of operators. In this work, we will introduce the basic ideas of dyadic Harmonic Analysis, which we use to build up to the main result we discuss on pointwise sparse domination, which is the Lerner–Ombrosi theorem. We also give applications of this theorem to some families of operators, mainly relating to singular integral operators. The text has been structured so as to motivate the introduction of new ideas through the lens of solving specific problems in Harmonic Analysis.

这篇说明性论文的目的是自成一体地介绍稀疏支配法。这种方法依赖于近年来备受关注的二元谐波分析技术。从本质上讲，它允许用一种统一的方法来证明大量算子的加权规范不等式。在本研究中，我们将介绍二元谐波分析的基本思想，并以此为基础，得出我们所讨论的关于点式稀疏支配的主要结果，即 Lerner-Ombrosi 定理。我们还给出了该定理在一些算子族中的应用，主要涉及奇异积分算子。这篇课文的结构是通过解决谐波分析中的具体问题来激励新思想的引入。

引用次数: 0

Digamma function and general Fischer series in the theory of Kempner sums 肯普纳和理论中的迪伽马函数和一般费歇尔级数

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae

Pub Date : 2024-09-02 DOI: 10.1016/j.exmath.2024.125604

The harmonic sum of the integers which are missing $p$ given digits in a base $b$ is expressed as $b log (b) / p$ plus corrections indexed by the excluded digits and expressed as integrals involving the digamma function and a suitable measure. A number of consequences are derived, such as explicit bounds, monotony, series representations and asymptotic expansions involving the zeta values at integers, and suitable moments of the measure. In the classic Kempner case of $b = 10$ and 9 as the only excluded digit, the series representation turns out to be exactly identical with a result obtained by Fischer already in 1993. Extending this work is indeed the goal of the present contribution.

在基数 b 中缺失 p 个给定数位的整数的谐和表示为 blog(b)/p 加上以缺失数位为索引的修正，并表示为涉及 digamma 函数和适当度量的积分。由此可以推导出许多结果，如明确的界限、单调性、涉及整数处zeta值的数列表示和渐近展开，以及量的适当矩。在 b=10 和 9 为唯一排除数字的经典坎普纳案例中，数列表示结果与费舍尔在 1993 年获得的结果完全相同。扩展这项工作正是本论文的目标。

引用次数: 0

Corrigendum to “A simple proof of the Wiener–Ikehara Tauberian Theorem” [Expo. Math. 42 (2024) 125570] 对 "维纳-池原陶伯定理的简单证明 "的更正 [Expo.

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae

Pub Date : 2024-08-09 DOI: 10.1016/j.exmath.2024.125603

引用次数: 0

An approach to annihilators in the context of vector field Lie algebras 向量场李代数中的湮没器方法

IF 0.7 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae

Pub Date : 2024-08-07 DOI: 10.1016/j.exmath.2024.125600

Charles H. Conley, William Goode

We present a general method for describing the annihilators of modules of Lie algebras under certain conditions, which hold for some tensor modules of vector field Lie algebras. As an example, we apply the method to obtain an efficient proof of previously known results on the annihilators of the bounded irreducible modules of .

我们提出了一种通用方法，用于描述在特定条件下李代数模块的湮没子，这些条件对于向量场李代数的某些张量模块是成立的。举例来说，我们运用该方法有效地证明了之前已知的关于 ...的有界不可还原模块的湮没子的结果。

引用次数: 0

Recent developments pertaining to Ramanujan’s formula for odd zeta values 拉马努扬奇数zeta值公式的最新进展

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae

Pub Date : 2024-08-02 DOI: 10.1016/j.exmath.2024.125602

In this expository article, we discuss the contributions made by several mathematicians with regard to a famous formula of Ramanujan for odd zeta values. The goal is to complement the excellent survey by Berndt and Straub (2017) with some of the recent developments that have taken place in the area in the last decade or so.

在这篇阐述性文章中，我们将讨论几位数学家对拉马努扬的一个著名奇数zeta值公式所做的贡献。我们的目标是，用过去十多年来该领域的一些最新进展来补充 Berndt 和 Straub（2017 年）的出色研究。

引用次数: 0

A complete Bernstein function related to the fractal dimension of Pascal’s pyramid modulo a prime 与帕斯卡金字塔模数素数分形维度相关的完整伯恩斯坦函数

IF 0.7 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae

Pub Date : 2024-08-02 DOI: 10.1016/j.exmath.2024.125601

Christian Berg

Let for . We prove that is a complete Bernstein function for and a Stieltjes function for . This answers a conjecture of David Bradley that is a Bernstein function when .

设为 .我们证明，，是一个完整的伯恩斯坦函数，并且，是一个斯蒂尔杰斯函数。这回答了戴维-布拉德利（David Bradley）的一个猜想，即当 . 是伯恩斯坦函数时， .

引用次数: 0

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