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Expositiones Mathematicae最新文献

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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
M. Ram Murty , Jagannath Sahoo , Akshaa Vatwani
{"title":"Corrigendum to “A simple proof of the Wiener–Ikehara Tauberian Theorem” [Expo. Math. 42 (2024) 125570]","authors":"M. Ram Murty , Jagannath Sahoo , Akshaa Vatwani","doi":"10.1016/j.exmath.2024.125603","DOIUrl":"10.1016/j.exmath.2024.125603","url":null,"abstract":"","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125603"},"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":"77 1","pages":""},"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
Atul Dixit
{"title":"Recent developments pertaining to Ramanujan’s formula for odd zeta values","authors":"Atul Dixit","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":"42 5","pages":"Article 125602"},"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":"56 1","pages":""},"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
Dicritical foliations and semiroots of plane branches 平面分支的二临界叶形和半根
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-18 DOI: 10.1016/j.exmath.2024.125591
Nuria Corral , Marcelo E. Hernandes , M.E. Rodrigues Hernandes
{"title":"Dicritical foliations and semiroots of plane branches","authors":"Nuria Corral ,&nbsp;Marcelo E. Hernandes ,&nbsp;M.E. Rodrigues Hernandes","doi":"10.1016/j.exmath.2024.125591","DOIUrl":"10.1016/j.exmath.2024.125591","url":null,"abstract":"<div><p>In this work we describe dicritical foliations in <span><math><mrow><mo>(</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span> at a triple point of the resolution dual graph of an analytic plane branch <span><math><mi>C</mi></math></span> using its semiroots. In particular, we obtain a constructive method to present a one-parameter family <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> of separatrices for such foliations. As a by-product we relate the contact order between a special member of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> and <span><math><mi>C</mi></math></span> with analytic discrete invariants of plane branches.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125591"},"PeriodicalIF":0.8,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000586/pdfft?md5=3299d7524f5c5d739013dc887d4e9582&pid=1-s2.0-S0723086924000586-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880878","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
Characterising the Haar measure on the [formula omitted]-adic rotation groups via inverse limits of measure spaces 通过度量空间的逆极限表征[公式省略]自旋群的哈氏度量
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-17 DOI: 10.1016/j.exmath.2024.125592
Paolo Aniello, Sonia L’Innocente, Stefano Mancini, Vincenzo Parisi, Ilaria Svampa, Andreas Winter
{"title":"Characterising the Haar measure on the [formula omitted]-adic rotation groups via inverse limits of measure spaces","authors":"Paolo Aniello, Sonia L’Innocente, Stefano Mancini, Vincenzo Parisi, Ilaria Svampa, Andreas Winter","doi":"10.1016/j.exmath.2024.125592","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125592","url":null,"abstract":"We determine the Haar measure on the compact -adic special orthogonal groups of rotations in dimension , by exploiting the machinery of inverse limits of measure spaces, for every prime . We characterise the groups as inverse limits of finite groups, of which we provide parametrisations and orders, together with an equivalent description through a multivariable Hensel lifting. Supplying these finite groups with their normalised counting measures, we get an inverse family of Haar measure spaces for each . Finally, we constructively prove the existence of the so-called inverse limit measure of these inverse families, which is explicitly computable, and prove that it gives the Haar measure on . Our results pave the way towards the study of the irreducible projective unitary representations of the -adic rotation groups, with potential applications to the recently proposed -adic quantum information theory.","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"120 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880872","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
Root involutions, real forms and diagrams 根渐开线、实数形式和图表
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-16 DOI: 10.1016/j.exmath.2024.125593
S. Marini , C. Medori , M. Nacinovich
{"title":"Root involutions, real forms and diagrams","authors":"S. Marini ,&nbsp;C. Medori ,&nbsp;M. Nacinovich","doi":"10.1016/j.exmath.2024.125593","DOIUrl":"10.1016/j.exmath.2024.125593","url":null,"abstract":"<div><p>We study the correspondence between equivalence classes of pairs consisting of real semisimple Lie algebras and their Cartan subalgebras and involutions of the corresponding root system. This can be graphically described by introducing <span><math><mrow><mi>S</mi><mspace></mspace></mrow></math></span>- and <span><math><mi>Σ</mi></math></span>-<em>diagrams</em>, generalizing those of Satake and Vogan.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125593"},"PeriodicalIF":0.8,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000604/pdfft?md5=445995afea316cbdb564083c3930d697&pid=1-s2.0-S0723086924000604-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141713250","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
Relative sectional category revisited 重新审视相对断面类别
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-11 DOI: 10.1016/j.exmath.2024.125590
J.M. García-Calcines
{"title":"Relative sectional category revisited","authors":"J.M. García-Calcines","doi":"10.1016/j.exmath.2024.125590","DOIUrl":"10.1016/j.exmath.2024.125590","url":null,"abstract":"<div><p>The concept of relative sectional category expands upon classical sectional category theory by incorporating the pullback of a fibration along a map. Our paper aims not only to explore this extension but also to thoroughly investigate its properties. We seek to uncover how the relative sectional category unifies several homotopic numerical invariants found in recent literature. These include the topological complexity of maps according to Murillo–Wu or Scott, relative topological complexity as defined by Farber, and homotopic distance for continuous maps in the sense of Macías-Virgós and Mosquera-Lois, among others.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125590"},"PeriodicalIF":0.8,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000574/pdfft?md5=e497014632089ab2358c7bdb9c539959&pid=1-s2.0-S0723086924000574-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736433","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
On ordinary isogeny graphs with level structures 关于具有水平结构的普通等值图
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-05 DOI: 10.1016/j.exmath.2024.125589
Antonio Lei , Katharina Müller
{"title":"On ordinary isogeny graphs with level structures","authors":"Antonio Lei ,&nbsp;Katharina Müller","doi":"10.1016/j.exmath.2024.125589","DOIUrl":"10.1016/j.exmath.2024.125589","url":null,"abstract":"<div><p>Let <span><math><mi>ℓ</mi></math></span> and <span><math><mi>p</mi></math></span> be two distinct prime numbers. We study <span><math><mi>ℓ</mi></math></span>-isogeny graphs of ordinary elliptic curves defined over a finite field of characteristic <span><math><mi>p</mi></math></span>, together with a level structure. Firstly, we show that as the level varies over all <span><math><mi>p</mi></math></span>-powers, the graphs form an Iwasawa-theoretic abelian <span><math><mi>p</mi></math></span>-tower, which can be regarded as a graph-theoretical analogue of the Igusa tower of modular curves. Secondly, we study the structure of the crater of these graphs, generalizing previous results on volcano graphs. Finally, we solve an inverse problem of graphs arising from the crater of <span><math><mi>ℓ</mi></math></span>-isogeny graphs with level structures, partially generalizing a recent result of Bambury, Campagna and Pazuki.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125589"},"PeriodicalIF":0.8,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000562/pdfft?md5=421a5d8db9c34e0de0dd8471dd9d689a&pid=1-s2.0-S0723086924000562-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736432","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
On convergence of points to limiting processes, with an application to zeta zeros 论点向极限过程的收敛，并应用于 zeta 零点
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-04 DOI: 10.1016/j.exmath.2024.125588
Juan Arias de Reyna , Brad Rodgers
{"title":"On convergence of points to limiting processes, with an application to zeta zeros","authors":"Juan Arias de Reyna ,&nbsp;Brad Rodgers","doi":"10.1016/j.exmath.2024.125588","DOIUrl":"10.1016/j.exmath.2024.125588","url":null,"abstract":"<div><p>This paper considers sequences of points on the real line which have been randomly translated, and provides conditions under which various notions of convergence to a limiting point process are equivalent. In particular we consider convergence in correlation, convergence in distribution, and convergence of spacings between points. We also prove a simple Tauberian theorem regarding rescaled correlations. The results are applied to zeros of the Riemann zeta-function to show that several ways to state the GUE Hypothesis are equivalent. The proof relies on a moment bound of A. Fujii.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125588"},"PeriodicalIF":0.8,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880857","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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