Mathematika最新文献

On type IV superorthogonality 关于IV型超正交

IF 0.8 3区数学

Mathematika Pub Date : 2025-10-01 DOI: 10.1112/mtk.70054

Jianghao Zhang

引用次数: 0

Upper bounds for moments of Dirichlet -functions to a fixed modulus 固定模的狄利克雷函数矩的上界

IF 0.8 3区数学

Mathematika Pub Date : 2025-09-30 DOI: 10.1112/mtk.70052

Peng Gao, Liangyi Zhao

引用次数: 0

Geometric inequalities, stability results and Kendall's problem in spherical space 球面空间中的几何不等式、稳定性结果和Kendall问题

IF 0.8 3区数学

Mathematika Pub Date : 2025-09-18 DOI: 10.1112/mtk.70049

Daniel Hug, Andreas Reichenbacher

{"title":"Geometric inequalities, stability results and Kendall's problem in spherical space","authors":"Daniel Hug, Andreas Reichenbacher","doi":"10.1112/mtk.70049","DOIUrl":"10.1112/mtk.70049","url":null,"abstract":"In Euclidean space, the asymptotic shape of large cells in various types of Poisson-driven random tessellations has been the subject of a famous conjecture due to David Kendall. Since shape is a geometric concept and large cells are identified by means of geometric size functionals, the resolution of the conjecture is inevitably connected with geometric inequalities of isoperimetric type and their improvements in the form of geometric stability results, relating geometric size functionals and hitting functionals. The latter are deterministic characteristics of the underlying random tessellation. The current work explores specific and typical cells of random tessellations in spherical space. A key ingredient of our approach is new geometric inequalities and quantitative strengthenings in terms of stability results for general and also for some specific size and hitting functionals of spherically convex bodies. As a consequence, we obtain probabilistic deviation inequalities and asymptotic distributions of quite general size functionals. In contrast to the Euclidean setting, where naturally the asymptotic regime concerns large size, in the spherical framework, the asymptotic analysis is primarily concerned with high intensities.","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70049","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145101941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Sparse bounds for discrete maximal functions associated with Birch–Magyar averages 与Birch-Magyar平均相关的离散极大函数的稀疏界

IF 0.8 3区数学

Mathematika Pub Date : 2025-09-12 DOI: 10.1112/mtk.70048

Ankit Bhojak, Surjeet Singh Choudhary, Siddhartha Samanta, Saurabh Shrivastava

引用次数: 0

New fiber and graph combinations of convex bodies 新的纤维和图形的凸体组合

IF 0.8 3区数学

Mathematika Pub Date : 2025-09-12 DOI: 10.1112/mtk.70043

Steven Hoehner, Sudan Xing

引用次数: 0

Higher rank antipodality 高阶反对性

IF 0.8 3区数学

Mathematika Pub Date : 2025-09-08 DOI: 10.1112/mtk.70046

Márton Naszódi, Zsombor Szilágyi, Mihály Weiner

{"title":"Higher rank antipodality","authors":"Márton Naszódi, Zsombor Szilágyi, Mihály Weiner","doi":"10.1112/mtk.70046","DOIUrl":"10.1112/mtk.70046","url":null,"abstract":"Motivated by general probability theory, we say that the set <math></math> in <math></math> is antipodal of rank <math></math>, if for any <math></math> elements <math></math>, there is an affine map from <math></math> to the <math></math>-dimensional simplex <math></math> that maps <math></math> bijectively onto the <math></math> vertices of <math></math>. For <math></math>, it coincides with the well-studied notion of (pairwise) antipodality introduced by Klee. We consider the following natural generalization of Klee's problem on antipodal sets: What is the maximum size of an antipodal set of rank <math></math> in <math></math>? We present a geometric characterization of antipodal sets of rank <math></math> and adapting the argument of Danzer and Grünbaum originally developed for the <math></math> case, we prove an upper bound which is exponential in the dimension. We show that this problem can be connected to a classical question in computer science on finding perfect hashes, and it provides a lower bound on the maximum size, which is also exponential in the dimension. By connecting rank-<math></math> antipodality to <math></math>-neighborly polytopes, we obtain another upper bound when <math></math>.","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70046","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

On the linear independence of -adic polygamma values 关于-进多值的线性无关性

IF 0.8 3区数学

Mathematika Pub Date : 2025-09-08 DOI: 10.1112/mtk.70040

Makoto Kawashima, Anthony Poëls

引用次数: 0

Fractional moments of -functions and sums of two squares in short intervals 函数的分数阶矩和短间隔内两个平方和

IF 0.8 3区数学

Mathematika Pub Date : 2025-09-04 DOI: 10.1112/mtk.70047

Siegfred Baluyot, Steven M. Gonek

引用次数: 0

On restricted sumsets with bounded degree relations 关于有界度关系的限制集合

IF 0.8 3区数学

Mathematika Pub Date : 2025-09-03 DOI: 10.1112/mtk.70045

Minghui Ouyang

{"title":"On restricted sumsets with bounded degree relations","authors":"Minghui Ouyang","doi":"10.1112/mtk.70045","DOIUrl":"10.1112/mtk.70045","url":null,"abstract":"Given two subsets <math></math> and a binary relation <math></math>, the restricted sumset of <math></math> with respect to <math></math> is defined as <math></math>. When <math></math> is taken as the equality relation, determining the minimum value of <math></math> is the famous Erdős–Heilbronn problem, which was solved separately by Dias da Silva, Hamidoune and Alon, Nathanson and Ruzsa. Lev later conjectured that if <math></math> with <math></math> and <math></math> is a matching between subsets of <math></math> and <math></math>, then <math></math>. We confirm this conjecture in the case where <math></math> for any <math></math>, provided that <math></math> for some sufficiently large <math></math> depending only on <math></math>. Our proof builds on a recent work by Bollobás, Leader, and Tiba, and a rectifiability argument developed by Green and Ruzsa. Furthermore, our method extends to cases when <math></math> is a degree-bounded relation, either on both sides <math></math> and <math></math> or solely on the smaller set. In addition, we construct subsets <math></math> with <math></math> such that <math></math> for any prime number <math></math>, where <math></math> is a matching on <math></math>. This extends an earlier construction by Lev and highlights a distinction between the combinatorial notion of the restricted sumset and the classcial Erdős–Heilbronn problem, where <math></math> holds given <math></math> is the equality relation on <math></math> and <math></math>.","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144935352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Topographs for binary quadratic forms and class numbers 二元二次型和类数的地形图

IF 0.8 3区数学

Mathematika Pub Date : 2025-09-01 DOI: 10.1112/mtk.70042

Cormac O'Sullivan

引用次数: 0