Indagationes Mathematicae-New Series最新文献

{"title":"Lq-spectrum of graph-directed self-similar measures that have overlaps and are essentially of finite type","authors":"Yuanyuan Xie","doi":"10.1016/j.indag.2025.05.013","DOIUrl":"10.1016/j.indag.2025.05.013","url":null,"abstract":"<div><div>For self-similar measures with overlaps, closed formulas of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span>-spectrum have been obtained by Ngai and the author for measures that are essentially of finite type in [J. Aust. Math. Soc. <strong>106</strong> (2019), 56–103]. We extend the results of Ngai and the author (Ngai and Xie, 2019) to graph-directed self-similar measures. For graph-directed self-similar measures satisfying the graph open set condition, the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span>-spectrum has been studied by Edgar and Mauldin (1992). The main novelty of our results is that the graph-directed self-similar measures we consider do not need to satisfy the graph open set condition. For graph-directed self-similar measures <span><math><mi>μ</mi></math></span> on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>\u0000 (<span><math><mrow><mi>d</mi><mo>≥</mo><mn>1</mn></mrow></math></span>), which could have overlaps but are essentially of finite type, we set up a framework for deriving a closed formula for the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span>-spectrum of <span><math><mi>μ</mi></math></span> for <span><math><mrow><mi>q</mi><mo>≥</mo><mn>0</mn></mrow></math></span>, and prove the differentiability of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span>-spectrum. The main ingredients of this framework include graph-directed self-similar measures that are strongly connected and not strongly connected and those in higher dimensions.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1355-1404"},"PeriodicalIF":0.8,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895928","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":"Square functions associated with RittE operators","authors":"Oualid Bouabdillah","doi":"10.1016/j.indag.2025.05.014","DOIUrl":"10.1016/j.indag.2025.05.014","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In a finite subset &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; of the torus &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;ℂ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, the notion of Ritt&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; operators on a Banach space and their functional calculus on generalized Stolz domains was developed and studied in Bouabdillah and Le Merdy (2024).&lt;/div&gt;&lt;div&gt;In this paper, we define a quadratic functional calculus for a Ritt&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; operator on &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, by a decomposition of type Franks–McIntosh. We show that with some hypothesis on the cotype of &lt;span&gt;&lt;math&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, this notion is equivalent to the existence of a bounded functional calculus on &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;div&gt;We define for a Ritt&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; operator on a Banach space &lt;span&gt;&lt;math&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and for any positive real number &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and for any &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;\u0000 &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mrow&gt;&lt;mo&gt;lim&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;munderover&gt;&lt;mrow&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ɛ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⊗&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;munderover&gt;&lt;mrow&gt;&lt;mo&gt;∏&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mo&gt;¯&lt;/mo&gt;&lt;/mover&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Rad&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; We show that, under the condition of finite cotype of &lt;span&gt;&lt;math&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, a Ritt&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; operator admits a quadratic functional calculus if and only if the estimates &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1417-1452"},"PeriodicalIF":0.8,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895930","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":"Pullback and Weil transfer on Chow groups","authors":"Nikita Karpenko,&nbsp;Guangzhao Zhu","doi":"10.1016/j.indag.2025.05.012","DOIUrl":"10.1016/j.indag.2025.05.012","url":null,"abstract":"<div><div>In the paper “Weil transfer of algebraic cycles”, published by the first author in Indagationes Mathematicae about 25 years ago, a <em>Weil transfer map</em> for Chow groups of smooth algebraic varieties has been constructed and its basic properties have been established. The proof of commutativity with the pullback homomorphisms given there used a variant of Moving Lemma suffering a lack of reference. Here we are providing an alternative proof based on a more contemporary construction of the pullback via a deformation to the normal cone.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1476-1480"},"PeriodicalIF":0.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895933","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":"On the triviality of m-modified conformal vector fields","authors":"Rahul Poddar ,&nbsp;Ramesh Sharma","doi":"10.1016/j.indag.2025.05.009","DOIUrl":"10.1016/j.indag.2025.05.009","url":null,"abstract":"<div><div>We prove that a compact Riemannian manifold <span><math><mi>M</mi></math></span> does not admit any non-trivial <span><math><mi>m</mi></math></span>-modified homothetic vector fields. In the corresponding case of an <span><math><mi>m</mi></math></span>-modified conformal vector field <span><math><mi>V</mi></math></span>, we establish an inequality that implies the triviality of <span><math><mi>V</mi></math></span>. Further, we demonstrate that an affine Killing <span><math><mi>m</mi></math></span>-modified conformal vector field on a non-compact Riemannian manifold <span><math><mi>M</mi></math></span> must be trivial. Finally, we show that an <span><math><mi>m</mi></math></span>-modified gradient conformal vector field is trivial under the assumptions of polynomial volume growth and convergence to zero at infinity.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1481-1490"},"PeriodicalIF":0.8,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895934","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 variant of the Linnik–Sprindžuk theorem for simple zeros of Dirichlet L-functions","authors":"William D. Banks","doi":"10.1016/j.indag.2025.05.007","DOIUrl":"10.1016/j.indag.2025.05.007","url":null,"abstract":"<div><div>For a primitive Dirichlet character <span><math><mi>X</mi></math></span>, a new hypothesis <span><math><mrow><msubsup><mrow><mi>RH</mi></mrow><mrow><mi>sim</mi></mrow><mrow><mi>†</mi></mrow></msubsup><mrow><mo>[</mo><mi>X</mi><mo>]</mo></mrow></mrow></math></span> is introduced, which asserts that (1) all <em>simple</em> zeros of <span><math><mrow><mi>L</mi><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> in the critical strip are located on the critical line, and (2) these zeros satisfy some specific conditions on their vertical distribution. We show that <span><math><mrow><msubsup><mrow><mi>RH</mi></mrow><mrow><mi>sim</mi></mrow><mrow><mi>†</mi></mrow></msubsup><mrow><mo>[</mo><mi>X</mi><mo>]</mo></mrow></mrow></math></span> (for any <span><math><mi>X</mi></math></span>) follows from the <em>generalized Riemann hypothesis</em>.</div><div>Assuming only the <em>generalized Lindelöf hypothesis</em>, we show that if <span><math><mrow><msubsup><mrow><mi>RH</mi></mrow><mrow><mi>sim</mi></mrow><mrow><mi>†</mi></mrow></msubsup><mrow><mo>[</mo><mi>X</mi><mo>]</mo></mrow></mrow></math></span><span> holds for one primitive character </span><span><math><mi>X</mi></math></span>, then it holds for <em>every</em> such <span><math><mi>X</mi></math></span>. If this occurs, then for every character <span><math><mi>χ</mi></math></span> (primitive or not), all simple zeros of <span><math><mrow><mi>L</mi><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>χ</mi><mo>)</mo></mrow></mrow></math></span> in the critical strip are located on the critical line. In particular, Siegel zeros cannot exist in this situation.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1459-1475"},"PeriodicalIF":0.8,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895932","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":"Note on a sum involving the divisor function","authors":"Liuying Wu","doi":"10.1016/j.indag.2025.05.006","DOIUrl":"10.1016/j.indag.2025.05.006","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>d</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> be the divisor function and denote by <span><math><mrow><mo>[</mo><mi>t</mi><mo>]</mo></mrow></math></span> the integral part of the real number <span><math><mi>t</mi></math></span>. In this paper, we prove that <span><math><mrow><munder><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>≤</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>1</mn><mo>/</mo><mi>c</mi></mrow></msup></mrow></munder><mi>d</mi><mfenced><mrow><mfenced><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><msup><mrow><mi>n</mi></mrow><mrow><mi>c</mi></mrow></msup></mrow></mfrac></mrow></mfenced></mrow></mfenced><mo>=</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mn>1</mn><mo>/</mo><mi>c</mi></mrow></msup><mo>+</mo><msub><mrow><mi>O</mi></mrow><mrow><mi>ɛ</mi><mo>,</mo><mi>c</mi></mrow></msub><mfenced><mrow><msup><mrow><mi>x</mi></mrow><mrow><mo>max</mo><mrow><mo>{</mo><mrow><mo>(</mo><mn>2</mn><mi>c</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mo>/</mo><mrow><mo>(</mo><mn>2</mn><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>5</mn><mi>c</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mo>,</mo><mn>5</mn><mo>/</mo><mrow><mo>(</mo><mn>5</mn><mi>c</mi><mo>+</mo><mn>6</mn><mo>)</mo></mrow><mo>}</mo></mrow><mo>+</mo><mi>ɛ</mi></mrow></msup></mrow></mfenced><mo>,</mo></mrow></math></span> where <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>k</mi><mo>≥</mo><mn>1</mn></mrow></msub><mi>d</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mfenced><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>k</mi></mrow><mrow><mn>1</mn><mo>/</mo><mi>c</mi></mrow></msup></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mrow><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mi>c</mi></mrow></msup></mrow></mfrac></mrow></mfenced></mrow></math></span> is a constant. This result constitutes an improvement upon that of Feng.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1453-1458"},"PeriodicalIF":0.8,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895931","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":"Pervasiveness of Lr(E,F) in Lr(E,Fδ)","authors":"Quinn Kiervin Starkey,&nbsp;Foivos Xanthos","doi":"10.1016/j.indag.2025.05.003","DOIUrl":"10.1016/j.indag.2025.05.003","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>E</mi><mo>,</mo><mi>F</mi></mrow></math></span> be Archimedean Riesz spaces, and let <span><math><msup><mrow><mi>F</mi></mrow><mrow><mi>δ</mi></mrow></msup></math></span> denote an order completion of <span><math><mi>F</mi></math></span>. In this note, we provide necessary conditions under which the space of all regular operators <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><mi>E</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span> is pervasive in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><mi>E</mi><mo>,</mo><msup><mrow><mi>F</mi></mrow><mrow><mi>δ</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>. Pervasiveness of <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><mi>E</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span> in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><mi>E</mi><mo>,</mo><msup><mrow><mi>F</mi></mrow><mrow><mi>δ</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> implies that the Riesz completion of <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><mi>E</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span> can be realized as a Riesz subspace of <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><mi>E</mi><mo>,</mo><msup><mrow><mi>F</mi></mrow><mrow><mi>δ</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>. It also ensures that the regular part of the space of order continuous operators <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>o</mi><mi>c</mi></mrow></msup><mrow><mo>(</mo><mi>E</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span> forms a band of <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><mi>E</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span>. Furthermore, the positive part <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> of any operator <span><math><mrow><mi>T</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><mi>E</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span>, provided it exists, is given by the Riesz–Kantorovich formula. The results apply in particular to cases where <span><math><mrow><mi>E</mi><mo>=</mo><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>∞</mi></mrow></msubsup></mrow></math></span>, <span><math><mrow><mi>E</mi><mo>=</mo><mi>c</mi></mrow></math></span>, or <span><math><mi>F</mi></math></span> is atomic, and they provide solutions to some problems posed in Abramovich and Wickstead (1991) and Wickstead (2024).</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1405-1416"},"PeriodicalIF":0.8,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895929","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":"Epimorphisms between finitely generated algebras","authors":"Luca Carai ,&nbsp;Miriam Kurtzhals ,&nbsp;Tommaso Moraschini","doi":"10.1016/j.indag.2025.04.006","DOIUrl":"10.1016/j.indag.2025.04.006","url":null,"abstract":"<div><div>A quasivariety has the <em>weak ES property</em> when the epimorphisms between its finitely generated members are surjective. A characterization of quasivarieties with the weak ES property is obtained and a method for detecting failures of this property in quasivarieties with a near unanimity term and in congruence permutable varieties is given. It is also shown that under reasonable assumptions the weak ES property implies arithmeticity. In particular, every filtral variety with the weak ES property is a discriminator variety.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1336-1354"},"PeriodicalIF":0.8,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144894971","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":"Bloch’s conjecture on certain surfaces of general type with pg=0 and with an involution: The Enriques case","authors":"Kalyan Banerjee","doi":"10.1016/j.indag.2025.04.002","DOIUrl":"10.1016/j.indag.2025.04.002","url":null,"abstract":"<div><div>In this short note we prove that an involution on certain examples of surfaces of general type with <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span>, acts as identity on the Chow group of zero cycles of the relevant surface. In particular we consider examples of such surfaces when the quotient is an Enriques surface and show that the Bloch conjecture holds for such surfaces.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1329-1335"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895926","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 graph-theoretic proof of Cobham’s Dichotomy for automatic sequences","authors":"Mieke Wessel","doi":"10.1016/j.indag.2025.04.001","DOIUrl":"10.1016/j.indag.2025.04.001","url":null,"abstract":"<div><div>We give a new graph-theoretic proof of a theorem of Cobham which says that the support of an automatic sequence is either sparse, that is, grows polylogarithmically, or grows at least like <span><math><msup><mrow><mi>N</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span> for some <span><math><mrow><mi>α</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. The proof uses the notions of tied vertices and cycle arborescences. With the ideas of the proof we can also give a new interpretation of the rank of a sparse sequence as the height of its cycle arborescence. In the non-sparse case we are able to show that the support has asymptotic behavior of the form <span><math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mi>B</mi></mrow></msup><mo>log</mo><msup><mrow><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>, where <span><math><mi>B</mi></math></span> turns out to be the logarithm of an integer root of a Perron number.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1310-1328"},"PeriodicalIF":0.8,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896433","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}