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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
Expositiones Mathematicae Pub Date : 2024-10-17 DOI: 10.1016/j.exmath.2024.125624
{"title":"A note on the standard zero-free region for L-functions","authors":"","doi":"10.1016/j.exmath.2024.125624","DOIUrl":"10.1016/j.exmath.2024.125624","url":null,"abstract":"<div><div>In this short note, we establish a standard zero-free region for a general class of <span><math><mi>L</mi></math></span>-functions for which their logarithms have coefficients with nonnegative real parts, including the Rankin–Selberg <span><math><mi>L</mi></math></span>-functions for unitary cuspidal automorphic representations.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142525776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Expositiones Mathematicae Pub Date : 2024-09-27 DOI: 10.1016/j.exmath.2024.125607
{"title":"Brownian motion in a vector space over a local field is a scaling limit","authors":"","doi":"10.1016/j.exmath.2024.125607","DOIUrl":"10.1016/j.exmath.2024.125607","url":null,"abstract":"<div><div>For any natural number <span><math><mi>d</mi></math></span>, the Vladimirov–Taibleson operator is a natural analogue of the Laplace operator for complex-valued functions on a <span><math><mi>d</mi></math></span>-dimensional vector space <span><math><mi>V</mi></math></span> over a local field <span><math><mi>K</mi></math></span>. Just as the Laplace operator on <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> is the infinitesimal generator of Brownian motion with state space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, the Vladimirov–Taibleson operator on <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>V</mi><mo>)</mo></mrow></mrow></math></span> is the infinitesimal generator of real-time Brownian motion with state space <span><math><mi>V</mi></math></span>. 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 <span><math><mi>V</mi></math></span> to be the <span><math><mi>p</mi></math></span>-adic numbers.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142432092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Expositiones Mathematicae Pub Date : 2024-09-26 DOI: 10.1016/j.exmath.2024.125619
{"title":"Abelian groups acting on the line","authors":"","doi":"10.1016/j.exmath.2024.125619","DOIUrl":"10.1016/j.exmath.2024.125619","url":null,"abstract":"<div><div>We study the action of finitely generated Abelian subgroups of <span><math><mrow><mi>H</mi><mi>o</mi><mi>m</mi><mi>e</mi><msub><mrow><mi>o</mi></mrow><mrow><mo>+</mo></mrow></msub><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>.</div><div>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.</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Expositiones Mathematicae Pub Date : 2024-09-16 DOI: 10.1016/j.exmath.2024.125616
{"title":"Some useful tools in the study of nonlinear elliptic problems","authors":"","doi":"10.1016/j.exmath.2024.125616","DOIUrl":"10.1016/j.exmath.2024.125616","url":null,"abstract":"<div><p>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 <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-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.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000835/pdfft?md5=7c5aee29b49c6102b8de52d2790f9ff3&pid=1-s2.0-S0723086924000835-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142271042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Expositiones Mathematicae Pub Date : 2024-09-04 DOI: 10.1016/j.exmath.2024.125605
{"title":"An introduction to pointwise sparse domination","authors":"","doi":"10.1016/j.exmath.2024.125605","DOIUrl":"10.1016/j.exmath.2024.125605","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000720/pdfft?md5=45dd60e1ad35b7a191fa8e59cc8e5e5d&pid=1-s2.0-S0723086924000720-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142271041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Expositiones Mathematicae Pub Date : 2024-09-02 DOI: 10.1016/j.exmath.2024.125604
{"title":"Digamma function and general Fischer series in the theory of Kempner sums","authors":"","doi":"10.1016/j.exmath.2024.125604","DOIUrl":"10.1016/j.exmath.2024.125604","url":null,"abstract":"<div><p>The harmonic sum of the integers which are missing <span><math><mi>p</mi></math></span> given digits in a base <span><math><mi>b</mi></math></span> is expressed as <span><math><mrow><mi>b</mi><mo>log</mo><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow><mo>/</mo><mi>p</mi></mrow></math></span> 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 <span><math><mrow><mi>b</mi><mo>=</mo><mn>10</mn></mrow></math></span> 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.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Expositiones Mathematicae Pub Date : 2024-08-09 DOI: 10.1016/j.exmath.2024.125603
{"title":"Corrigendum to “A simple proof of the Wiener–Ikehara Tauberian Theorem” [Expo. Math. 42 (2024) 125570]","authors":"","doi":"10.1016/j.exmath.2024.125603","DOIUrl":"10.1016/j.exmath.2024.125603","url":null,"abstract":"","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000707/pdfft?md5=155e4832fa776ce893a5d10e1db35394&pid=1-s2.0-S0723086924000707-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141963641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Expositiones Mathematicae Pub Date : 2024-08-07 DOI: 10.1016/j.exmath.2024.125600
Charles H. Conley, William Goode
{"title":"An approach to annihilators in the context of vector field Lie algebras","authors":"Charles H. Conley, William Goode","doi":"10.1016/j.exmath.2024.125600","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125600","url":null,"abstract":"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 .","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Expositiones Mathematicae Pub Date : 2024-08-02 DOI: 10.1016/j.exmath.2024.125602
{"title":"Recent developments pertaining to Ramanujan’s formula for odd zeta values","authors":"","doi":"10.1016/j.exmath.2024.125602","DOIUrl":"10.1016/j.exmath.2024.125602","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Expositiones Mathematicae Pub Date : 2024-08-02 DOI: 10.1016/j.exmath.2024.125601
Christian Berg
{"title":"A complete Bernstein function related to the fractal dimension of Pascal’s pyramid modulo a prime","authors":"Christian Berg","doi":"10.1016/j.exmath.2024.125601","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125601","url":null,"abstract":"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 .","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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