{"title":"Classification of tight contact structures on some Seifert fibered manifolds","authors":"Tanushree Shah","doi":"10.1016/j.indag.2025.03.011","DOIUrl":"10.1016/j.indag.2025.03.011","url":null,"abstract":"<div><div>We classify tight contact structures with zero Giroux torsion on some Seifert-fibered manifolds with four exceptional fibers. We get the lower bound by constructing contact structures using Legendrian surgery. We use convex surface theory to obtain the upper bound.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1288-1309"},"PeriodicalIF":0.8,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896432","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 note on the distribution of clusters and deserts of prime numbers","authors":"Eugenio P. Balanzario","doi":"10.1016/j.indag.2025.03.007","DOIUrl":"10.1016/j.indag.2025.03.007","url":null,"abstract":"<div><div>We consider the distribution of values of weighted sums of the von Mangoldt arithmetical function. Using a formula for the distribution of values of trigonometric polynomials, we are able to present evidence supporting the claim that these weighted sums follow a distribution with a normal-like behavior.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1276-1287"},"PeriodicalIF":0.8,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896431","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":"Conditions for the difference set of a central Cantor set to be a Cantorval. Part II","authors":"Piotr Nowakowski","doi":"10.1016/j.indag.2025.03.005","DOIUrl":"10.1016/j.indag.2025.03.005","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo>⊂</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span> be the central Cantor set generated by a sequence <span><math><mrow><mi>a</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mfenced><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span>. It is known that the difference set <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo>−</mo><mi>C</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow></mrow></math></span> has one of three possible forms: a finite union of closed intervals, a Cantor set, or a Cantorval. In the previous paper (Filipczak and Nowakowski, 2023), there was given the sufficient condition for the sequence <span><math><mi>a</mi></math></span>, which implies that <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo>−</mo><mi>C</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow></mrow></math></span> is a Cantorval. In this paper we give different conditions for a sequence <span><math><mi>a</mi></math></span>, which guarantee the same assertion. We also prove a corollary, which provides infinitely many new examples of Cantorvals.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1223-1244"},"PeriodicalIF":0.8,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896430","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":"Non-self-intersective Dragon curves","authors":"Shigeki Akiyama , Yuichi Kamiya , Fan Wen","doi":"10.1016/j.indag.2025.03.006","DOIUrl":"10.1016/j.indag.2025.03.006","url":null,"abstract":"<div><div>Let us fold a strip of paper many times in the same direction, and then unfold it to form a fixed angle <span><math><mi>θ</mi></math></span> at all creases. The resulting shape is called the Dragon curve with the unfolding angle <span><math><mi>θ</mi></math></span>. When <span><math><mrow><mn>0</mn><mo>≤</mo><mi>θ</mi><mo><</mo><mn>90</mn><mo>°</mo></mrow></math></span>, the corresponding Dragon curve has a self-intersection. When <span><math><mrow><mi>θ</mi><mo>=</mo><mn>180</mn><mo>°</mo></mrow></math></span>, the corresponding Dragon curve is a straight line, which has no self-intersection. In this paper, we will show that any Dragon curve whose unfolding angle is greater than <span><math><mrow><mn>99</mn><mo>.</mo><mn>3438</mn><mo>°</mo></mrow></math></span> and less than <span><math><mrow><mn>180</mn><mo>°</mo></mrow></math></span> has no self-intersection.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1245-1275"},"PeriodicalIF":0.8,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895927","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 arithmetically defined hyperbolic 5-manifolds arising from maximal orders in definite Q-algebras","authors":"Joachim Schwermer","doi":"10.1016/j.indag.2025.03.001","DOIUrl":"10.1016/j.indag.2025.03.001","url":null,"abstract":"<div><div>Using the quaternionic formalism for the description of the group of isometries of hyperbolic 5-space we consider arithmetically defined 5-dimensional hyperbolic manifolds which are non-compact but of finite volume. They arise from maximal orders <span><math><mi>Λ</mi></math></span> in the central simple algebra <span><math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span> of degree 4 where <span><math><mi>D</mi></math></span> denotes a definite quaternion <span><math><mi>Q</mi></math></span>-algebra. The affine <span><math><mi>Z</mi></math></span>-group scheme <span><math><mrow><mi>S</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>Λ</mi></mrow></msub></mrow></math></span> determines an integral structure for the algebraic <span><math><mi>Q</mi></math></span>-group <span><math><mrow><mi>G</mi><mo>=</mo><mi>S</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>Λ</mi></mrow></msub><msub><mrow><mo>×</mo></mrow><mrow><mi>Z</mi></mrow></msub><mi>Q</mi></mrow></math></span> obtained by base change. The group <span><math><mi>G</mi></math></span> is an inner form of the special linear <span><math><mi>Q</mi></math></span>-group <span><math><mrow><mi>S</mi><msub><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math></span>. Each torsion-free subgroup <span><math><mrow><mi>Γ</mi><mo>⊂</mo><mi>S</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>Λ</mi></mrow></msub><mrow><mo>(</mo><mi>Z</mi><mo>)</mo></mrow></mrow></math></span> determines a hyperbolic 5-manifold, to be denoted <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>/</mo><mi>Γ</mi></mrow></math></span>. Given a principal congruence subgroup <span><math><mrow><mi>Γ</mi><mrow><mo>(</mo><msup><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>, we determine the number of ends and the dimensions of the cohomology groups at infinity of the manifold <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>/</mo><mi>Γ</mi><mrow><mo>(</mo><msup><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1205-1222"},"PeriodicalIF":0.8,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896429","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}
G. Bezhanishvili , F. Dashiell Jr. , M.A. Moshier , J. Walters-Wayland
{"title":"Degrees of join-distributivity via Bruns–Lakser towers","authors":"G. Bezhanishvili , F. Dashiell Jr. , M.A. Moshier , J. Walters-Wayland","doi":"10.1016/j.indag.2025.02.005","DOIUrl":"10.1016/j.indag.2025.02.005","url":null,"abstract":"<div><div>We utilize the Bruns–Lakser completion to introduce Bruns–Lakser towers of a meet-semilattice. This machinery enables us to develop various hierarchies inside the class of bounded distributive lattices, which measure <span><math><mi>κ</mi></math></span>-degrees of distributivity of bounded distributive lattices and their Dedekind–MacNeille completions. We also use Priestley duality to obtain a dual characterization of the resulting hierarchies. Among other things, this yields a natural generalization of Esakia’s representation of Heyting lattices to proHeyting lattices.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1180-1204"},"PeriodicalIF":0.8,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896427","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":"Binary quadratic forms with the same value set","authors":"Étienne Fouvry , Peter Koymans","doi":"10.1016/j.indag.2025.01.005","DOIUrl":"10.1016/j.indag.2025.01.005","url":null,"abstract":"<div><div>Given a binary quadratic form <span><math><mrow><mi>F</mi><mo>∈</mo><mi>Z</mi><mrow><mo>[</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>]</mo></mrow></mrow></math></span>, we define its value set <span><math><mrow><mi>F</mi><mrow><mo>(</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> to be <span><math><mrow><mo>{</mo><mi>F</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>:</mo><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>}</mo></mrow></math></span>. If <span><math><mrow><mi>F</mi><mo>,</mo><mi>G</mi><mo>∈</mo><mi>Z</mi><mrow><mo>[</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>]</mo></mrow></mrow></math></span> are two binary quadratic forms, we give necessary and sufficient conditions on <span><math><mi>F</mi></math></span> and <span><math><mi>G</mi></math></span> for <span><math><mrow><mi>F</mi><mrow><mo>(</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>=</mo><mi>G</mi><mrow><mo>(</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1157-1179"},"PeriodicalIF":0.8,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896426","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 moments of the error term of the multivariable kth divisor functions","authors":"Zhen Guo, Xin Li","doi":"10.1016/j.indag.2025.01.003","DOIUrl":"10.1016/j.indag.2025.01.003","url":null,"abstract":"<div><div>Suppose <span><math><mrow><mi>k</mi><mo>⩾</mo><mn>3</mn></mrow></math></span> is an integer. Let <span><math><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> be the number of ways <span><math><mi>n</mi></math></span> can be written as a product of <span><math><mi>k</mi></math></span> fixed factors. For any fixed integer <span><math><mrow><mi>r</mi><mo>⩾</mo><mn>2</mn></mrow></math></span>, we have the asymptotic formula <span><span><span><math><mrow><munder><mrow><mo>∑</mo></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mspace></mspace><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>⩽</mo><mi>x</mi></mrow></munder><msub><mrow><mi>τ</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>r</mi></mrow></msup><munderover><mrow><mo>∑</mo></mrow><mrow><mi>ℓ</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>r</mi><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></munderover><msub><mrow><mi>d</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>ℓ</mi></mrow></msub><msup><mrow><mrow><mo>(</mo><mo>log</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>ℓ</mi></mrow></msup><mo>+</mo><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>+</mo><mi>ɛ</mi></mrow></msup><mo>)</mo></mrow><mo>,</mo></mrow></math></span></span></span>where <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>ℓ</mi></mrow></msub></math></span> and <span><math><mrow><mn>0</mn><mo><</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>k</mi></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span> are computable constants. In this paper we study the mean square of <span><math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and give upper bounds for <span><math><mrow><mi>k</mi><mo>⩾</mo><mn>4</mn></mrow></math></span> and an asymptotic formula for the mean square of <span><math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>r</mi><mo>,</mo><mn>3</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>. We also get an upper bound for the third power moment of <span><math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>r</mi><mo>,</mo><mn>3</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>. Moreover, we study the first power moment of <span><math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>r</mi><mo>,</mo><mn>3</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and then give a result for the sign ","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1133-1156"},"PeriodicalIF":0.8,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896428","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":"An elementary proof of the Benjamini–Nekrashevych–Pete conjecture for the semi-direct products Zn⋊Z","authors":"Dean Wardell","doi":"10.1016/j.indag.2025.01.002","DOIUrl":"10.1016/j.indag.2025.01.002","url":null,"abstract":"<div><div>A finitely generated group <span><math><mi>G</mi></math></span> is called strongly scale-invariant if there exists an injective homomorphism <span><math><mrow><mi>f</mi><mo>:</mo><mi>G</mi><mo>→</mo><mi>G</mi></mrow></math></span> such that <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> is a finite index subgroup of <span><math><mi>G</mi></math></span> and such that <span><math><mrow><msub><mrow><mo>∩</mo></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub><msup><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> is finite. Nekrashevych and Pete conjectured that all strongly scale-invariant groups are virtually nilpotent, after disproving a stronger conjecture by Benjamini.</div><div>This conjecture is known to be true in some situations. Deré proved it for virtually polycyclic groups. In this paper, we provide an elementary proof for those polycyclic groups that can be written as a semi-direct product <span><math><mrow><msup><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>⋊</mo><mi>Z</mi></mrow></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 5","pages":"Pages 1125-1132"},"PeriodicalIF":0.8,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896425","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":"Additive spectrum preserving mappings fromvon Neumann algebras","authors":"Martin Mathieu , Francois Schulz","doi":"10.1016/j.indag.2024.12.005","DOIUrl":"10.1016/j.indag.2024.12.005","url":null,"abstract":"<div><div>We establish Jafarian’s 2009 conjecture that every additive spectrum preserving mapping from a von Neumann algebra onto a semisimple Banach algebra is a Jordan isomorphism.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 4","pages":"Pages 1112-1123"},"PeriodicalIF":0.5,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270627","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}
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