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Distribution of integer points on determinant surfaces and a mod-p analogue 行列式曲面上整数点的分布及模p模拟
IF 0.8 3区 数学
Mathematika Pub Date : 2026-04-13 DOI: 10.1112/mtk.70093
Satadal Ganguly, Rachita Guria
{"title":"Distribution of integer points on determinant surfaces and a mod-p analogue","authors":"Satadal Ganguly,&nbsp;Rachita Guria","doi":"10.1112/mtk.70093","DOIUrl":"10.1112/mtk.70093","url":null,"abstract":"<p>We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form <span></span><math></math>, where <span></span><math></math> is a non-zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables <span></span><math></math> as well as of <span></span><math></math>. We also establish an asymptotic formula for counting integer solutions with smooth weights to the congruence <span></span><math></math>, where <span></span><math></math> is a large prime, with a strong bound on the error term.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70093","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147683708","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
The Steklov spectrum of spherical cylinders 球形圆柱体的斯特克洛夫谱
IF 0.8 3区 数学
Mathematika Pub Date : 2026-04-08 DOI: 10.1112/mtk.70092
Spencer Bullent
{"title":"The Steklov spectrum of spherical cylinders","authors":"Spencer Bullent","doi":"10.1112/mtk.70092","DOIUrl":"10.1112/mtk.70092","url":null,"abstract":"<p>The Steklov problem on a compact Lipschitz domain is to find harmonic functions on the interior whose outward normal derivative on the boundary is some multiple (eigenvalue) of their trace on the boundary. These eigenvalues form the Steklov spectrum of the domain. This article considers the Steklov spectrum of spherical cylinders (Euclidean ball times interval). It is shown that the spectral counting function admits a two-term asymptotic expansion. The coefficient of the second term consists of a contribution from the curvature of the boundary and a contribution from the edges.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70092","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147683511","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
Khintchine-type theorems for weighted uniform inhomogeneous approximations via transference principle 基于迁移原理的加权一致非齐次逼近的khintchine型定理
IF 0.8 3区 数学
Mathematika Pub Date : 2026-04-06 DOI: 10.1112/mtk.70089
Vasiliy Neckrasov
{"title":"Khintchine-type theorems for weighted uniform inhomogeneous approximations via transference principle","authors":"Vasiliy Neckrasov","doi":"10.1112/mtk.70089","DOIUrl":"10.1112/mtk.70089","url":null,"abstract":"<p>In 2019 Kleinbock and Wadleigh proved a “zero-one law” for uniform inhomogeneous Diophantine approximations. We generalize this statement to arbitrary weight functions and establish a new and simple proof of this statement, based on the transference principle. We also give a complete description of the sets of <span></span><math></math>-Dirichlet pairs with a fixed matrix in this setthe up from Lebesgue measure point of view. As an application, we consider the set of badly approximable matrices and give a characterization of bad approximability in terms of inhomogeneous approximations. All the aforementioned metrical descriptions work (and sometimes can be strengthened) for weighted Diophantine approximations.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70089","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147683299","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
Dimension bounds for singular affine forms 奇异仿射形式的维限
IF 0.8 3区 数学
Mathematika Pub Date : 2026-04-03 DOI: 10.1112/mtk.70084
Gaurav Aggarwal
{"title":"Dimension bounds for singular affine forms","authors":"Gaurav Aggarwal","doi":"10.1112/mtk.70084","DOIUrl":"10.1112/mtk.70084","url":null,"abstract":"<p>In this paper, we establish upper bounds on the dimension of sets of singular-on-average and <span></span><math></math>-singular affine forms in singly metric settings where either the matrix or the shift is fixed. These results partially address open questions posed by Das, Fishman, Simmons, and Urbański, as well as Kleinbock and Wadleigh. Furthermore, we extend our results to the generalized weighted setup and derive bounds for the intersection of these sets with a wide class of fractals.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147683130","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
Failure of stability of a maximal operator bound for perturbed Nevo–Thangavelu means 扰动neo - thangavelu均值的极大算子界稳定性失效
IF 0.8 3区 数学
Mathematika Pub Date : 2026-04-01 DOI: 10.1112/mtk.70090
Jaehyeon Ryu, Andreas Seeger
{"title":"Failure of stability of a maximal operator bound for perturbed Nevo–Thangavelu means","authors":"Jaehyeon Ryu,&nbsp;Andreas Seeger","doi":"10.1112/mtk.70090","DOIUrl":"10.1112/mtk.70090","url":null,"abstract":"<p>Let <span></span><math></math> be a two-step nilpotent Lie group, identified via the exponential map with the Lie-algebra <span></span><math></math>, where <span></span><math></math>. We consider maximal functions associated to spheres in a <span></span><math></math>-dimensional linear subspace <span></span><math></math>, dilated by the automorphic dilations. <span></span><math></math> boundedness results for the case where <span></span><math></math> are well understood. Here, we consider the case of a tilted hyperplane <span></span><math></math> which is not invariant under the automorphic dilations. In the case of Métivier groups, it is known that the <span></span><math></math>-boundedness results are stable under a small linear tilt. We show that this is generally not the case for other two-step groups, and provide new necessary conditions for <span></span><math></math> boundedness. We prove these results in a more general setting with tilted versions of submanifolds of <span></span><math></math>.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682875","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
The -mean of the exponential sum of 指数和的-均值
IF 0.8 3区 数学
Mathematika Pub Date : 2026-04-01 DOI: 10.1112/mtk.70088
Tomos Parry
{"title":"The -mean of the exponential sum of","authors":"Tomos Parry","doi":"10.1112/mtk.70088","DOIUrl":"10.1112/mtk.70088","url":null,"abstract":"<p>We use the classical circle method to give a relatively simple proof that\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682877","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
Mixed moments of Hecke eigenforms and -functions Hecke特征形式与-函数的混合矩
IF 0.8 3区 数学
Mathematika Pub Date : 2026-04-01 DOI: 10.1112/mtk.70091
Bingrong Huang
{"title":"Mixed moments of Hecke eigenforms and -functions","authors":"Bingrong Huang","doi":"10.1112/mtk.70091","DOIUrl":"10.1112/mtk.70091","url":null,"abstract":"<p>In this paper, we establish estimates for the expectation and variance of the mixed (2,2)-moment of two Hecke eigenforms of distinct weights. Our results yield applications to triple product <span></span><math></math>-functions. The proofs are based on moments of <span></span><math></math>-functions.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682876","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
Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set 在属于给定集合的具有连续部分商的数集合上支持测度的傅里叶衰减
IF 0.8 3区 数学
Mathematika Pub Date : 2026-03-30 DOI: 10.1112/mtk.70087
Robert Fraser
{"title":"Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set","authors":"Robert Fraser","doi":"10.1112/mtk.70087","DOIUrl":"10.1112/mtk.70087","url":null,"abstract":"<p>We consider measures supported on sets of irrational numbers possessing many consecutive partial quotients satisfying a condition based on the previous partial quotients. We show that under mild assumptions, such sets will always support measures whose Fourier transform decays to zero.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665885","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
Flat grazes of convex bodies and local characterization of quadrics 凸体的平面放牧与二次曲面的局部特征
IF 0.8 3区 数学
Mathematika Pub Date : 2026-03-25 DOI: 10.1112/mtk.70086
Jesús Jerónimo-Castro, Luis Montejano, Efrén Morales-Amaya
{"title":"Flat grazes of convex bodies and local characterization of quadrics","authors":"Jesús Jerónimo-Castro,&nbsp;Luis Montejano,&nbsp;Efrén Morales-Amaya","doi":"10.1112/mtk.70086","DOIUrl":"https://doi.org/10.1112/mtk.70086","url":null,"abstract":"<p>We prove several local characterizations of quadrics, among them, the local Blaschke's Theorem, and use this result to give some characterizations of the ellipsoid related to the flatness of its grazes.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569056","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
Flat grazes of convex bodies and local characterization of quadrics 凸体的平面放牧与二次曲面的局部特征
IF 0.8 3区 数学
Mathematika Pub Date : 2026-03-25 DOI: 10.1112/mtk.70086
Jesús Jerónimo-Castro, Luis Montejano, Efrén Morales-Amaya
{"title":"Flat grazes of convex bodies and local characterization of quadrics","authors":"Jesús Jerónimo-Castro,&nbsp;Luis Montejano,&nbsp;Efrén Morales-Amaya","doi":"10.1112/mtk.70086","DOIUrl":"https://doi.org/10.1112/mtk.70086","url":null,"abstract":"<p>We prove several local characterizations of quadrics, among them, the local Blaschke's Theorem, and use this result to give some characterizations of the ellipsoid related to the flatness of its grazes.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569252","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
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