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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
Products of boundary classes on M¯0,n via balanced weights 通过平衡加权的 M¯0,n 上边界类的乘积
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-01 DOI: 10.1016/j.exmath.2024.125587
Maria Gillespie , Jake Levinson
{"title":"Products of boundary classes on M¯0,n via balanced weights","authors":"Maria Gillespie ,&nbsp;Jake Levinson","doi":"10.1016/j.exmath.2024.125587","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125587","url":null,"abstract":"<div><p>In this note, we give a simple closed formula for an arbitrary product, landing in dimension 0, of boundary classes on the Deligne–Mumford moduli space <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></msub></math></span>. For any such boundary strata <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></mrow></msub></mrow></math></span>, we show the intersection product <span><math><mrow><mo>∫</mo><msubsup><mrow><mo>∏</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>ℓ</mi></mrow></msubsup><mrow><mo>[</mo><msub><mrow><mi>X</mi></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>]</mo></mrow></mrow></math></span> is either a signed product of multinomial coefficients, or zero, and provide a simple criterion for determining when it is nonzero.</p><p>We do not claim originality for our product formula, but to our knowledge it does not appear elsewhere in the literature.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 4","pages":"Article 125587"},"PeriodicalIF":0.8,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141486747","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
Harmonic analysis of compact Lie supergroups 紧凑李超群的谐波分析
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-01 DOI: 10.1016/j.exmath.2024.125586
M.-K. Chuah, C.A. Cremonini, R. Fioresi
{"title":"Harmonic analysis of compact Lie supergroups","authors":"M.-K. Chuah, C.A. Cremonini, R. Fioresi","doi":"10.1016/j.exmath.2024.125586","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125586","url":null,"abstract":"We realize the irreducible representations of a compact Lie supergroup , with a contragredient simple Lie superalgebra, in the space of square integrable (in the sense of Berezin) holomorphic sections on , is the real torus in the complexification of . We give an explicit realization of unitary representations when .","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"29 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614865","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 survey on conjugacy class graphs of groups 群的共轭类图概览
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-06-04 DOI: 10.1016/j.exmath.2024.125585
Peter J. Cameron , Firdous Ee Jannat , Rajat Kanti Nath , Reza Sharafdini
{"title":"A survey on conjugacy class graphs of groups","authors":"Peter J. Cameron ,&nbsp;Firdous Ee Jannat ,&nbsp;Rajat Kanti Nath ,&nbsp;Reza Sharafdini","doi":"10.1016/j.exmath.2024.125585","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125585","url":null,"abstract":"<div><p>There are several graphs defined on groups. Among them we consider graphs whose vertex set consists conjugacy classes of a group <span><math><mi>G</mi></math></span> and adjacency is defined by properties of the elements of conjugacy classes. In particular, we consider commuting/nilpotent/solvable conjugacy class graph of <span><math><mi>G</mi></math></span> where two distinct conjugacy classes <span><math><msup><mrow><mi>a</mi></mrow><mrow><mi>G</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>b</mi></mrow><mrow><mi>G</mi></mrow></msup></math></span> are adjacent if there exist some elements <span><math><mrow><mi>x</mi><mo>∈</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>G</mi></mrow></msup></mrow></math></span> and <span><math><mrow><mi>y</mi><mo>∈</mo><msup><mrow><mi>b</mi></mrow><mrow><mi>G</mi></mrow></msup></mrow></math></span> such that <span><math><mrow><mo>〈</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>〉</mo></mrow></math></span> is abelian/nilpotent/solvable. After a section of introductory results and examples, we discuss all the available results on connectedness, graph realization, genus, various spectra and energies of certain induced subgraphs of these graphs. Proofs of the results are not included. However, many open problems for further investigation are stated.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 4","pages":"Article 125585"},"PeriodicalIF":0.7,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000525/pdfft?md5=18b445b3245dc9583ae34dc4fb72277e&pid=1-s2.0-S0723086924000525-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141303423","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
Proofs of ergodicity of piecewise Möbius interval maps using planar extensions 利用平面扩展证明片断莫比乌斯区间映射的遍历性
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-05-15 DOI: 10.1016/j.exmath.2024.125575
Kariane Calta , Cor Kraaikamp , Thomas A. Schmidt
{"title":"Proofs of ergodicity of piecewise Möbius interval maps using planar extensions","authors":"Kariane Calta ,&nbsp;Cor Kraaikamp ,&nbsp;Thomas A. Schmidt","doi":"10.1016/j.exmath.2024.125575","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125575","url":null,"abstract":"<div><p>We give two results for deducing dynamical properties of piecewise Möbius interval maps from their related planar extensions. First, eventual expansivity and the existence of an ergodic invariant probability measure equivalent to Lebesgue measure both follow from mild finiteness conditions on the planar extension along with a new property “bounded non-full range” used to relax traditional Markov conditions. Second, the “quilting” operation to appropriately nearby planar systems, introduced by Kraaikamp and co-authors, can be used to prove several key dynamical properties of a piecewise Möbius interval map. As a proof of concept, we apply these results to recover known results on the well-studied Nakada <span><math><mi>α</mi></math></span>-continued fractions; we obtain similar results for interval maps derived from an infinite family of non-commensurable Fuchsian groups.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 4","pages":"Article 125575"},"PeriodicalIF":0.7,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141164254","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
Geometric characterization of Ahlfors regular spaces in terms of dyadic cubes related to wavelets with its applications to equivalences of Lipschitz spaces 用与小波相关的二元立方体描述阿赫福斯规则空间的几何特征，并将其应用于等价利普齐兹空间
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-05-13 DOI: 10.1016/j.exmath.2024.125574
Fan Wang , Dachun Yang , Wen Yuan
{"title":"Geometric characterization of Ahlfors regular spaces in terms of dyadic cubes related to wavelets with its applications to equivalences of Lipschitz spaces","authors":"Fan Wang ,&nbsp;Dachun Yang ,&nbsp;Wen Yuan","doi":"10.1016/j.exmath.2024.125574","DOIUrl":"10.1016/j.exmath.2024.125574","url":null,"abstract":"<div><p>Assume that <span><math><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></math></span> is a space of homogeneous type introduced by R. R. Coifman and G. Weiss. In this article, the authors establish a geometric characterization of Ahlfors regular spaces via the dyadic cubes constructed by T. Hytönen and A. Kairema. As applications, the authors show that Lipschitz spaces defined via the quasi-metric under consideration and Lipschitz spaces defined via the measure under consideration coincide with equivalent norms if and only if <span><math><mi>X</mi></math></span> is an Ahlfors regular space. Moreover, the authors also prove that Lipschitz spaces defined via the quasi-metric under consideration and Campanato spaces defined via balls coincide with equivalent norms if and only if <span><math><mi>X</mi></math></span> is an Ahlfors regular space.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 4","pages":"Article 125574"},"PeriodicalIF":0.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141040800","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
Periodicity of general multidimensional continued fractions using repetend matrix form 使用重复矩阵形式的一般多维续分数的周期性
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-04-04 DOI: 10.1016/j.exmath.2024.125571
Hanka Řada , Štěpán Starosta , Vítězslav Kala
{"title":"Periodicity of general multidimensional continued fractions using repetend matrix form","authors":"Hanka Řada ,&nbsp;Štěpán Starosta ,&nbsp;Vítězslav Kala","doi":"10.1016/j.exmath.2024.125571","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125571","url":null,"abstract":"<div><p>We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend and use it to prove that a number of vectors have an eventually periodic expansion in the Algebraic Jacobi–Perron algorithm. Further, we give criteria for vectors to have purely periodic expansions; in particular, the vector cannot be totally positive.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 3","pages":"Article 125571"},"PeriodicalIF":0.7,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140554317","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 note on the base-p expansions of putative counterexamples to the p-adic Littlewood conjecture 关于 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e27" altimg="si13.svg" 假设反例的基点展开的说明
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-03-20 DOI: 10.1016/j.exmath.2024.125548
J. Blackman , S. Kristensen , M.J. Northey
{"title":"A note on the base-p expansions of putative counterexamples to the p-adic Littlewood conjecture","authors":"J. Blackman ,&nbsp;S. Kristensen ,&nbsp;M.J. Northey","doi":"10.1016/j.exmath.2024.125548","DOIUrl":"10.1016/j.exmath.2024.125548","url":null,"abstract":"<div><p>In this paper, we investigate the base-<span><math><mi>p</mi></math></span> expansions of putative counterexamples to the <span><math><mi>p</mi></math></span>-adic Littlewood conjecture of de Mathan and Teulié. We show that if a counterexample exists, then so does a counterexample whose base-<span><math><mi>p</mi></math></span> expansion is uniformly recurrent. Furthermore, we show that if the base-<span><math><mi>p</mi></math></span> expansion of <span><math><mi>x</mi></math></span> is a morphic word <span><math><mrow><mi>τ</mi><mrow><mo>(</mo><msup><mrow><mi>φ</mi></mrow><mrow><mi>ω</mi></mrow></msup><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> where <span><math><mrow><msup><mrow><mi>φ</mi></mrow><mrow><mi>ω</mi></mrow></msup><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow></mrow></math></span> contains a subword of the form <span><math><mrow><mi>u</mi><mi>X</mi><mi>u</mi><mi>X</mi><mi>u</mi></mrow></math></span> with <span><math><mrow><msub><mrow><mo>lim</mo></mrow><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></msub><mrow><mo>|</mo><msup><mrow><mi>φ</mi></mrow><mrow><mi>n</mi></mrow></msup><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>|</mo></mrow><mo>=</mo><mi>∞</mi></mrow></math></span>, then <span><math><mi>x</mi></math></span> satisfies the <span><math><mi>p</mi></math></span>-adic Littlewood conjecture. In the special case when <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn></mrow></math></span>, we show that the conjecture holds for all pure morphic words.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 3","pages":"Article 125548"},"PeriodicalIF":0.7,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S072308692400015X/pdfft?md5=9882f79608644e821115bc0ed83923d6&pid=1-s2.0-S072308692400015X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140281675","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
Abstract embeddability ranks 抽象可嵌入性等级
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-03-18 DOI: 10.1016/j.exmath.2024.125563
Florent P. Baudier , Christian Rosendal
{"title":"Abstract embeddability ranks","authors":"Florent P. Baudier ,&nbsp;Christian Rosendal","doi":"10.1016/j.exmath.2024.125563","DOIUrl":"10.1016/j.exmath.2024.125563","url":null,"abstract":"<div><p>We describe several ordinal indices that are capable of detecting, according to various metric notions of faithfulness, the embeddability between pairs of Polish spaces. These embeddability ranks are of theoretical interest but seem difficult to estimate in practice. Embeddability ranks, which are easier to estimate in practice, are embeddability ranks generated by Schauder bases. These embeddability ranks are inspired by the nonlinear indices à la Bourgain. In particular, we resolve a problem raised by F. Baudier, G. Lancien, P. Motakis, and Th. Schlumprecht in Coarse and Lipschitz universality, Fund. Math. 254 (2021), no. 2, 181–214, regarding the necessity of additional set-theoretic axioms regarding the main coarse universality result there.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 3","pages":"Article 125563"},"PeriodicalIF":0.7,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140182011","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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