Indagationes Mathematicae-New Series最新文献

{"title":"Non-trivial integer solutions of xr+yr=Dzp","authors":"Yasemin Kara,&nbsp;Diana Mocanu,&nbsp;Ekin Özman","doi":"10.1016/j.indag.2025.11.001","DOIUrl":"10.1016/j.indag.2025.11.001","url":null,"abstract":"<div><div>In this paper, we use the modular method over totally real fields together with some standard conjectures (the Weak Frey–Mazur Conjecture and the Eichler–Shimura Conjecture) to prove that infinitely many equations of the type <span><math><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>=</mo><mi>D</mi><msup><mrow><mi>z</mi></mrow><mrow><mi>p</mi></mrow></msup></mrow></math></span> do not have any non-trivial primitive integer solutions, where <span><math><mrow><mi>r</mi><mo>≥</mo><mn>5</mn></mrow></math></span> is a fixed prime, whenever <span><math><mi>p</mi></math></span> is large enough. For <span><math><mrow><mi>r</mi><mo>≡</mo><mn>3</mn><mspace></mspace><mrow><mo>(</mo><mo>mod</mo><mspace></mspace><mn>4</mn><mo>)</mo></mrow></mrow></math></span>, we get the same result only assuming the Weak Frey–Mazur Conjecture.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1510-1523"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546614","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":"On the integrability of Lie algebroids by diffeological spaces","authors":"Joel Villatoro","doi":"10.1016/j.indag.2025.07.011","DOIUrl":"10.1016/j.indag.2025.07.011","url":null,"abstract":"<div><div>Lie’s third theorem does not hold for Lie groupoids and Lie algebroids. In this article, we show that Lie’s third theorem is valid within a specific class of diffeological groupoids that we call ‘singular Lie groupoids.’ To achieve this, we introduce a subcategory of diffeological spaces which we call ‘quasi-etale.’ Singular Lie groupoids are precisely the groupoid objects within this category, where the unit space is a manifold.</div><div>Our approach involves the construction of a functor that maps singular Lie groupoids to Lie algebroids, extending the classical functor from Lie groupoids to Lie algebroids. We prove that the Ševera–Weinstein groupoid of an algebroid is an example of a singular Lie groupoid, thereby establishing Lie’s third theorem in this context.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1192-1242"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546653","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":"Moment formulas of Siegel transforms with congruence conditions in dimension 2","authors":"Jiyoung Han,&nbsp;Seul Bee Lee","doi":"10.1016/j.indag.2025.10.003","DOIUrl":"10.1016/j.indag.2025.10.003","url":null,"abstract":"<div><div>We compute the first and second moment formulas for Siegel transforms in connection with problems of counting primitive lattice points in the real plane with congruence conditions. For applications, we define the cone of the relative homogeneous space and extend the moment formulas over this setting. As applications, we derive an analog of Schmidt’s random counting theorem and the quantitative Khintchine theorem for irrational numbers, approximated by rational numbers <span><math><mrow><mi>p</mi><mo>/</mo><mi>q</mi></mrow></math></span>, where we place a congruence-conditional constraint on the vector <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1431-1449"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546619","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":"Least energy solutions of two asymptotically cubic Kirchhoff equations on locally finite graphs","authors":"Zhangyi Yu,&nbsp;Xingyong Zhang,&nbsp;Xin Ou","doi":"10.1016/j.indag.2025.12.001","DOIUrl":"10.1016/j.indag.2025.12.001","url":null,"abstract":"<div><div>We study the existence of least energy solutions for two Kirchhoff equations with the asymptotically cubic nonlinearity <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>λ</mi><mi>u</mi><mo>+</mo><mi>η</mi><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi></mrow></math></span> on a weighted, connected, and locally finite graph <span><math><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span>. Such nonlinearity satisfies neither <span><math><mrow><mfrac><mrow><mi>F</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow><mrow><msup><mrow><mi>u</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></mfrac><mo>→</mo><mo>+</mo><mi>∞</mi></mrow></math></span> as <span><math><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mo>→</mo><mi>∞</mi></mrow></math></span>, where <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mi>u</mi></mrow></msubsup><mi>f</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mi>d</mi><mi>s</mi></mrow></math></span>, nor <span><math><mrow><mfrac><mrow><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow><mrow><mi>u</mi></mrow></mfrac><mo>→</mo><mn>0</mn></mrow></math></span> as <span><math><mrow><mi>u</mi><mo>→</mo><mn>0</mn></mrow></math></span>. By utilizing the constrained variational method, we prove that there exist <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≥</mo><mn>0</mn></mrow></math></span>\u0000 (<span><math><mrow><msubsup><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>∗</mo></mrow></msubsup><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><msubsup><mrow><mi>η</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>∗</mo></mrow></msubsup><mo>≥</mo><mn>0</mn></mrow></math></span>) such that these two equations have at least one least energy solution if <span><math><mrow><mrow><mo>|</mo><mi>λ</mi><mo>|</mo></mrow><mo>&lt;</mo><mi>a</mi><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span>\u0000 (<span><math><mrow><mrow><mo>|</mo><mi>λ</mi><mo>|</mo></mrow><mo>&lt;</mo><mi>a</mi><msubsup><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>∗</mo></mrow></msubsup></mrow></math></span>) and <span><math><mrow><mi>η</mi><mo>&gt;</mo><msub><mrow><mi>η</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>\u0000 (<span><math><mrow><mi>η</mi><mo>&gt;</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>∗</mo></mrow></msubsup></mrow></math></span>).</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1604-1619"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546546","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":"Geometric properties of periodic lattices in function fields","authors":"Noy Soffer Aranov","doi":"10.1016/j.indag.2025.12.002","DOIUrl":"10.1016/j.indag.2025.12.002","url":null,"abstract":"<div><div>Periodic lattices are natural generalizations of lattices, which arise naturally in diophantine approximations with rationals of bounded denominators. In this paper, we prove analogues of classical theorems in geometry of numbers for periodic lattices in function fields. Moreover, we use special matrices to compute the covering and packing radii of special periodic lattices.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1620-1633"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546620","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":"Determining explicitly the Mordell–Weil group of certain rational elliptic surfaces","authors":"Remke Kloosterman","doi":"10.1016/j.indag.2025.09.001","DOIUrl":"10.1016/j.indag.2025.09.001","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>A</mi><mo>,</mo><mi>B</mi></mrow></math></span> be nonzero rational numbers. Consider the elliptic curve <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>A</mi><mo>,</mo><mi>B</mi></mrow></msub><mo>/</mo><mi>Q</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> with Weierstrass equation <span><math><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mi>A</mi><msup><mrow><mi>t</mi></mrow><mrow><mn>6</mn></mrow></msup><mo>+</mo><mi>B</mi></mrow></math></span>.</div><div>An algorithm to determine <span><math><mrow><mo>rank</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>A</mi><mo>,</mo><mi>B</mi></mrow></msub><mrow><mo>(</mo><mi>Q</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> as a function of <span><math><mrow><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></mrow></math></span> was presented in a recent paper Desjardins and Naskręcki (2024). We will give a different and shorter proof for the correctness of that algorithm, using a more geometric approach and discuss for which classes of examples the approach by Desjardins and Naskręcki (2024) might be useful.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1243-1249"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546654","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":"On the distribution of SL(2,N)-saturated Farey fractions","authors":"Jack Anderson,&nbsp;Florin P. Boca,&nbsp;Cristian Cobeli,&nbsp;Alexandru Zaharescu","doi":"10.1016/j.indag.2025.11.004","DOIUrl":"10.1016/j.indag.2025.11.004","url":null,"abstract":"<div><div>We consider the set <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>Q</mi></mrow></msub></math></span> of Farey fractions <span><math><mrow><mi>d</mi><mo>/</mo><mi>b</mi></mrow></math></span> of order <span><math><mi>Q</mi></math></span> with the property that there exists a matrix <span><math><mrow><mfenced><mrow><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mrow></mfenced><mo>∈</mo><mo>SL</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>Z</mi><mo>)</mo></mrow></mrow></math></span> of trace at most <span><math><mi>Q</mi></math></span>, with positive entries and <span><math><mrow><mi>a</mi><mo>≥</mo><mo>max</mo><mrow><mo>{</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>}</mo></mrow></mrow></math></span>. For every <span><math><mrow><mi>Q</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, the set <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>Q</mi></mrow></msub><mo>∪</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow></mrow></math></span> is shown to define a unimodular partition of the interval <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span>. We also prove that the elements of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>Q</mi></mrow></msub></math></span> are asymptotically distributed with respect to the probability measure with density <span><math><mrow><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow><mo>−</mo><mn>1</mn><mo>/</mo><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>/</mo><mo>log</mo><mrow><mo>(</mo><mn>4</mn><mo>/</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span> and that the sequence of sets <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>Q</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>Q</mi></mrow></msub></math></span> has a limiting gap distribution as <span><math><mrow><mi>Q</mi><mo>→</mo><mi>∞</mi></mrow></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1586-1603"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546616","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 problem of Hirst for the Hurwitz continued fraction and the Hausdorff dimension of sets with restricted slowly growing digits","authors":"Yuto Nakajima,&nbsp;Hiroki Takahasi","doi":"10.1016/j.indag.2025.09.008","DOIUrl":"10.1016/j.indag.2025.09.008","url":null,"abstract":"<div><div>We address the problem of determining the Hausdorff dimension of sets consisting of complex irrationals whose complex continued fraction digits satisfy prescribed restrictions and growth conditions. For the Hurwitz continued fraction, we confirm Hirst’s conjecture, as a complex analogue of the result of Wang and Wu (2008) for the regular continued fraction. We also prove a complex analogue of the second-named author’s result on the Hausdorff dimension of sets with restricted slowly growing digits (Takahasi, 2023). To these ends, we exploit an infinite conformal iterated function system associated with the Hurwitz continued fraction.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1322-1340"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546609","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":"The Albanese morphism for hyperelliptic varieties","authors":"Pieter Belmans,&nbsp;Andreas Demleitner,&nbsp;Pedro Núñez","doi":"10.1016/j.indag.2025.10.004","DOIUrl":"10.1016/j.indag.2025.10.004","url":null,"abstract":"<div><div>We explicitly describe the Albanese morphism of a hyperelliptic variety, i.e., the quotient <span><math><mi>X</mi></math></span> of an abelian variety <span><math><mi>A</mi></math></span> by a finite group <span><math><mi>G</mi></math></span> acting freely and not only by translations, by giving a description of the Albanese variety and the Albanese fibers in terms of <span><math><mi>A</mi></math></span> and <span><math><mi>G</mi></math></span>. In particular, the fibers are themselves abelian or hyperelliptic varieties, and we investigate which can occur in explicit examples. As an application we show that the derived category of <span><math><mi>X</mi></math></span> is indecomposable in certain cases.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1450-1475"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546611","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":"Semiflows on finite topological spaces","authors":"Pedro J. Chocano","doi":"10.1016/j.indag.2025.10.006","DOIUrl":"10.1016/j.indag.2025.10.006","url":null,"abstract":"<div><div>In this paper, we study flows and semiflows defined on any given finite topological <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-space <span><math><mi>X</mi></math></span>. We show that there exist non-trivial semiflows on <span><math><mi>X</mi></math></span>, unless <span><math><mi>X</mi></math></span> is a minimal finite space. Specifically, non-trivial semiflows exist if and only if <span><math><mi>X</mi></math></span> contains down beat points, and a non-trivial semiflow is essentially a strong deformation retraction. As a consequence of this result, we provide a new and concise proof that the only flow that can be defined on <span><math><mi>X</mi></math></span> is the trivial flow. Finally, we discuss the number of different semiflows that can be defined on <span><math><mi>X</mi></math></span> in terms of down beat points and other special points.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1500-1509"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546613","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}