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Pure point diffraction and entropy beyond the Euclidean space 超越欧几里得空间的纯点衍射和熵
IF 0.5 4区 数学
Indagationes Mathematicae-New Series Pub Date : 2024-09-01 DOI: 10.1016/j.indag.2024.07.003
T. Hauser
{"title":"Pure point diffraction and entropy beyond the Euclidean space","authors":"T. Hauser","doi":"10.1016/j.indag.2024.07.003","DOIUrl":"10.1016/j.indag.2024.07.003","url":null,"abstract":"<div><p>For Euclidean pure point diffractive Delone sets of finite local complexity and with uniform patch frequencies it is well known that the patch counting entropy computed along the closed centred balls is zero. We consider such sets in the setting of <span><math><mi>σ</mi></math></span>-compact locally compact Abelian groups and show that the topological entropy of the associated Delone dynamical system is zero. For this we provide a suitable version of the variational principle. We furthermore construct counterexamples, which show that the patch counting entropy of such sets can be non-zero in this context. Other counterexamples will show that the patch counting entropy of such a set cannot be computed along a limit and even be infinite in this setting.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"35 5","pages":"Pages 1057-1074"},"PeriodicalIF":0.5,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0019357724000818/pdfft?md5=37da9342f84d0427094033cf2fe72940&pid=1-s2.0-S0019357724000818-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142121806","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
Gap labels for zeros of the partition function of the 1D Ising model via the Schwartzman homomorphism 通过施瓦茨曼同构实现一维伊辛模型分区函数零点的间隙标签
IF 0.5 4区 数学
Indagationes Mathematicae-New Series Pub Date : 2024-09-01 DOI: 10.1016/j.indag.2023.05.004
{"title":"Gap labels for zeros of the partition function of the 1D Ising model via the Schwartzman homomorphism","authors":"","doi":"10.1016/j.indag.2023.05.004","DOIUrl":"10.1016/j.indag.2023.05.004","url":null,"abstract":"<div><p>Inspired by the 1995 paper of Baake–Grimm–Pisani, we aim to explain the empirical observation that the distribution of Lee–Yang zeros corresponding to a one-dimensional Ising model<span> appears to follow the gap labelling theorem. This follows by combining two main ingredients: first, the relation between the transfer matrix formalism for the 1D Ising model and an ostensibly unrelated matrix formalism generating the Szegő recursion for orthogonal polynomials on the unit circle, and second, the gap labelling theorem for CMV matrices.</span></p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"35 5","pages":"Pages 813-836"},"PeriodicalIF":0.5,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134992589","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
Generalized hypergeometric functions with several variables 具有多个变量的广义超几何函数
IF 0.5 4区 数学
Indagationes Mathematicae-New Series Pub Date : 2024-07-25 DOI: 10.1016/j.indag.2024.07.007
Saiei-Jaeyeong Matsubara-Heo , Toshio Oshima
{"title":"Generalized hypergeometric functions with several variables","authors":"Saiei-Jaeyeong Matsubara-Heo ,&nbsp;Toshio Oshima","doi":"10.1016/j.indag.2024.07.007","DOIUrl":"10.1016/j.indag.2024.07.007","url":null,"abstract":"<div><div>We introduce a hypergeometric series with several variables, which generalizes Appell’s, Lauricella’s and Kempé de Fériet’s hypergeometric series, and study the system of differential equations that it satisfies. We determine the singularities, the rank and the condition for the reducibility of the system. We give complete local solutions of the system at many singular points of the system and solve the connection problem among these local solutions. Under some assumptions, the system is written as a KZ-type equation. We determine its spectral type in the direction of coordinates as well as simultaneous eigenspace decompositions of residue matrices. The system may or may not be rigid in the sense of N. Katz viewed as an ordinary differential equation in some direction. We also show that the system is a special case of Gel’fand–Kapranov–Zelevinsky system. From this point of view, we discuss multivariate generalizations.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 2","pages":"Pages 507-566"},"PeriodicalIF":0.5,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141847679","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 D-module approach to invariant distributions with finitely many orbits
IF 0.5 4区 数学
Indagationes Mathematicae-New Series Pub Date : 2024-07-15 DOI: 10.1016/j.indag.2024.07.006
Hiroyuki Ochiai
{"title":"A D-module approach to invariant distributions with finitely many orbits","authors":"Hiroyuki Ochiai","doi":"10.1016/j.indag.2024.07.006","DOIUrl":"10.1016/j.indag.2024.07.006","url":null,"abstract":"<div><div>Tauchi provides an example illustrating the action of a real algebraic subgroup <span><math><mi>H</mi></math></span> of <span><math><mrow><mi>G</mi><mi>L</mi><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> with finitely many orbits on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup></math></span>, while the dimension of the space of relative <span><math><mi>H</mi></math></span>-invariant distributions on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup></math></span> is infinite. We offer a perspective on this example from the viewpoint of D-modules, where we explicitly determine the simple quotient regular holonomic D-modules and demonstrate that the distributions exhibit an enlarged symmetry.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 2","pages":"Pages 497-506"},"PeriodicalIF":0.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463560","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
Simple singularity of type E7 and the complex reflection group ST34 E7 型简单奇点和复反射群 ST34
IF 0.5 4区 数学
Indagationes Mathematicae-New Series Pub Date : 2024-07-15 DOI: 10.1016/j.indag.2024.07.008
Jiro Sekiguchi
{"title":"Simple singularity of type E7 and the complex reflection group ST34","authors":"Jiro Sekiguchi","doi":"10.1016/j.indag.2024.07.008","DOIUrl":"10.1016/j.indag.2024.07.008","url":null,"abstract":"<div><div>This paper studies a family of surfaces of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> which is a deformation of a simple singularity of type <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>7</mn></mrow></msub></math></span>. This family has six parameters which are regarded as basic invariants of the complex reflection group No. 34 in the list of the paper of Shephard and Todd (1954). We compute 1-parameter subfamilies of the family in question corresponding to corank one reflection subgroups of No. 34 group. In particular, we determine the types of simple singularities on the surfaces appearing in this manner.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 2","pages":"Pages 567-592"},"PeriodicalIF":0.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141714375","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 Stone–von Neumann equivalence of categories for smooth representations of the Heisenberg group 海森堡群光滑表示的斯通-冯-诺依曼等价范畴
IF 0.5 4区 数学
Indagationes Mathematicae-New Series Pub Date : 2024-07-08 DOI: 10.1016/j.indag.2024.07.001
Raul Gomez , Dmitry Gourevitch , Siddhartha Sahi
{"title":"A Stone–von Neumann equivalence of categories for smooth representations of the Heisenberg group","authors":"Raul Gomez ,&nbsp;Dmitry Gourevitch ,&nbsp;Siddhartha Sahi","doi":"10.1016/j.indag.2024.07.001","DOIUrl":"10.1016/j.indag.2024.07.001","url":null,"abstract":"<div><div>The classical Stone–von Neumann theorem relates the irreducible unitary representations of the Heisenberg group <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> to non-trivial unitary characters of its center <span><math><mi>Z</mi></math></span>, and plays a crucial role in the construction of the oscillator representation for the metaplectic group. In this paper we extend these ideas to non-unitary and non-irreducible representations, thereby obtaining an equivalence of categories between certain representations of <span><math><mi>Z</mi></math></span> and those of <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Our main result is a smooth equivalence, which involves the fundamental ideas of du Cloux on differentiable representations and smooth imprimitivity systems for Nash groups. We show how to extend the oscillator representation to the smooth setting and give an application to degenerate Whittaker models for representations of reductive groups. We also include an algebraic equivalence, which can be regarded as a generalization of Kashiwara’s lemma from the theory of <span><math><mi>D</mi></math></span>-modules.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 2","pages":"Pages 450-481"},"PeriodicalIF":0.5,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141710853","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 Lp-factorizations of representations 关于表征的 Lp 因子化的说明
IF 0.5 4区 数学
Indagationes Mathematicae-New Series Pub Date : 2024-07-06 DOI: 10.1016/j.indag.2024.07.002
Pritam Ganguly, Bernhard Krötz, Job J. Kuit
{"title":"A note on Lp-factorizations of representations","authors":"Pritam Ganguly,&nbsp;Bernhard Krötz,&nbsp;Job J. Kuit","doi":"10.1016/j.indag.2024.07.002","DOIUrl":"10.1016/j.indag.2024.07.002","url":null,"abstract":"<div><div>In this paper we give an overview on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-factorizations of Lie group representations and introduce the notion of smooth <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-factorization.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 2","pages":"Pages 482-496"},"PeriodicalIF":0.5,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717121","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
Qℓ-cohomology projective planes from Enriques surfaces in odd characteristic 奇特征恩里克曲面的Qℓ-同调投影面
IF 0.5 4区 数学
Indagationes Mathematicae-New Series Pub Date : 2024-07-01 DOI: 10.1016/j.indag.2024.01.007
Matthias Schütt
{"title":"Qℓ-cohomology projective planes from Enriques surfaces in odd characteristic","authors":"Matthias Schütt","doi":"10.1016/j.indag.2024.01.007","DOIUrl":"10.1016/j.indag.2024.01.007","url":null,"abstract":"<div><p>We give a complete classification of <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></math></span>-cohomology projective planes with isolated ADE-singularities and numerically trivial canonical bundle in odd characteristic. This leads to a beautiful relation with certain Enriques surfaces which parallels the situation in characteristic zero, yet displays intriguing subtleties.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"35 4","pages":"Pages 744-767"},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0019357724000077/pdfft?md5=3c3aaaef3ddd511c727a0f394e98674a&pid=1-s2.0-S0019357724000077-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139763532","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
Ranks of elliptic curves in cyclic sextic extensions of Q Q 的循环六元扩展中的椭圆曲线秩
IF 0.5 4区 数学
Indagationes Mathematicae-New Series Pub Date : 2024-07-01 DOI: 10.1016/j.indag.2024.01.004
Hershy Kisilevsky , Masato Kuwata
{"title":"Ranks of elliptic curves in cyclic sextic extensions of Q","authors":"Hershy Kisilevsky ,&nbsp;Masato Kuwata","doi":"10.1016/j.indag.2024.01.004","DOIUrl":"10.1016/j.indag.2024.01.004","url":null,"abstract":"<div><p><span>For an elliptic curve </span><span><math><mrow><mi>E</mi><mo>/</mo><mi>Q</mi></mrow></math></span> we show that there are infinitely many cyclic sextic extensions <span><math><mrow><mi>K</mi><mo>/</mo><mi>Q</mi></mrow></math></span> such that the Mordell–Weil group <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>K</mi><mo>)</mo></mrow></mrow></math></span> has rank greater than the subgroup of <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>K</mi><mo>)</mo></mrow></mrow></math></span> generated by all the <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span> for the proper subfields <span><math><mrow><mi>F</mi><mo>⊂</mo><mi>K</mi></mrow></math></span>. For certain curves <span><math><mrow><mi>E</mi><mo>/</mo><mi>Q</mi></mrow></math></span> we show that the number of such fields <span><math><mi>K</mi></math></span> of conductor less than <span><math><mi>X</mi></math></span> is <span><math><mrow><mo>≫</mo><msqrt><mrow><mi>X</mi></mrow></msqrt></mrow></math></span>.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"35 4","pages":"Pages 728-743"},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139551961","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
Computing the Weil representation of a superelliptic curve 计算超椭圆曲线的 Weil 表示
IF 0.5 4区 数学
Indagationes Mathematicae-New Series Pub Date : 2024-07-01 DOI: 10.1016/j.indag.2024.01.002
Irene I. Bouw, Duc Khoi Do, Stefan Wewers
{"title":"Computing the Weil representation of a superelliptic curve","authors":"Irene I. Bouw,&nbsp;Duc Khoi Do,&nbsp;Stefan Wewers","doi":"10.1016/j.indag.2024.01.002","DOIUrl":"10.1016/j.indag.2024.01.002","url":null,"abstract":"<div><p>We study the Weil representation <span><math><mi>ρ</mi></math></span> of a curve over a <span><math><mi>p</mi></math></span>-adic field with potential reduction of compact type. We show that <span><math><mi>ρ</mi></math></span> can be reconstructed from its stable reduction. For superelliptic curves of the form <span><math><mrow><msup><mrow><mi>y</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> at primes <span><math><mi>p</mi></math></span> whose residue characteristic is prime to the exponent <span><math><mi>n</mi></math></span> we make this explicit.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"35 4","pages":"Pages 708-727"},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0019357724000028/pdfft?md5=a98632bbf32b4580b4c64c774c1f6a96&pid=1-s2.0-S0019357724000028-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139506875","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
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