Indagationes Mathematicae-New Series最新文献

{"title":"Correlation functions of the Rudin–Shapiro sequence","authors":"","doi":"10.1016/j.indag.2023.03.003","DOIUrl":"10.1016/j.indag.2023.03.003","url":null,"abstract":"<div><p><span>In this paper, we show that all odd-point correlation functions of the balanced Rudin–Shapiro sequence vanish and that all even-point correlation functions depend only on a single number, which holds for any weighted correlation function as well. For the four-point correlation functions, we provide a more detailed exposition which reveals some arithmetic structures and symmetries. In particular, we show that one can obtain the autocorrelation coefficients of its topological factor with maximal </span>pure point spectrum among them.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44470250","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}

{"title":"A characterisation of linear repetitivity for cut and project sets with general polytopal windows","authors":"","doi":"10.1016/j.indag.2024.03.003","DOIUrl":"10.1016/j.indag.2024.03.003","url":null,"abstract":"<div><p>The cut and project method is a central construction in the theory of Aperiodic Order for generating quasicrystals with pure point diffraction. Linear repetitivity (<strong>LR</strong>) is a form of ideal regularity of aperiodic patterns. Recently, Koivusalo and the present author characterised <strong>LR</strong> for cut and project sets with convex polytopal windows whose supporting hyperplanes are commensurate with the lattice, the weak homogeneity property. For such cut and project sets, we show that <strong>LR</strong> is equivalent to two properties. One is a low complexity condition, which may be determined from the cut and project data by calculating the ranks of the intersections of the projection of the lattice to the internal space with the subspaces parallel to the supporting hyperplanes of the window. The second condition is that the projection of the lattice to the internal space is Diophantine (or ‘badly approximable’), which loosely speaking means that the lattice points in the total space stay far from the physical space, relative to their norm. We review then extend these results to non-convex and disconnected polytopal windows, as well as windows with polytopal partitions producing cut and project sets of labelled points. Moreover, we obtain a complete characterisation of <strong>LR</strong> in the fully general case, where weak homogeneity is not assumed. Here, the Diophantine property must be replaced with an inhomogeneous analogue. We show that cut and project schemes with internal space isomorphic to <span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>⊕</mo><mi>G</mi><mo>⊕</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>r</mi></mrow></msup></mrow></math></span>, for <span><math><mi>G</mi></math></span> finite Abelian, can, up to MLD equivalence, be reduced to ones with internal space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, so our results also cover cut and project sets of this form, such as the (generalised) Penrose tilings.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0019357724000156/pdfft?md5=2746cea224983adf4877799dace1bad2&pid=1-s2.0-S0019357724000156-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203437","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}

{"title":"Pure point diffraction and entropy beyond the Euclidean space","authors":"","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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"title":"Regular models of hyperelliptic curves","authors":"Simone Muselli","doi":"10.1016/j.indag.2023.12.001","DOIUrl":"10.1016/j.indag.2023.12.001","url":null,"abstract":"<div><p>Let <span><math><mi>K</mi></math></span> be a complete discretely valued field of residue characteristic not 2 and <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> its ring of integers. We explicitly construct a regular model over <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> with strict normal crossings of any hyperelliptic curve <span><math><mrow><mi>C</mi><mo>/</mo><mi>K</mi><mo>:</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>. For this purpose, we introduce the new notion of <em>MacLane cluster picture</em>, that aims to be a link between clusters and MacLane valuations.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0019357723001040/pdfft?md5=04ca296b6016027d47af6c7c64f21d09&pid=1-s2.0-S0019357723001040-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555115","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}

{"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":null,"pages":null},"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}

{"title":"Curves over finite fields and arithmetic and geometry of K3 surfaces: Celebrating Jaap Top’s 60th anniversary","authors":"Remke Kloosterman (Managing Editor),&nbsp;Steffen Müller,&nbsp;Cecília Salgado,&nbsp;Lenny Taelman","doi":"10.1016/j.indag.2024.06.006","DOIUrl":"https://doi.org/10.1016/j.indag.2024.06.006","url":null,"abstract":"","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141582268","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}

{"title":"Counterexamples to the Hasse Principle among the twists of the Klein quartic","authors":"Elisa Lorenzo García ,&nbsp;Michaël Vullers","doi":"10.1016/j.indag.2023.08.007","DOIUrl":"10.1016/j.indag.2023.08.007","url":null,"abstract":"<div><p>In this paper we inspect from closer the local and global points of the twists of the Klein quartic. For the local ones we use geometric arguments, while for the global ones we strongly use the modular interpretation of the twists. The main result is providing families with (conjecturally infinitely many) twists of the Klein quartic that are counterexamples to the Hasse Principle.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0019357723000848/pdfft?md5=03e46a5dbb56004e38e7926d976cb7c3&pid=1-s2.0-S0019357723000848-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944511","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}