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Lower bounds for the large deviations of Selberg's central limit theorem
IF 0.8 3区 数学
Mathematika Pub Date : 2024-12-11 DOI: 10.1112/mtk.70002
Louis-Pierre Arguin, Emma Bailey
{"title":"Lower bounds for the large deviations of Selberg's central limit theorem","authors":"Louis-Pierre Arguin,&nbsp;Emma Bailey","doi":"10.1112/mtk.70002","DOIUrl":"https://doi.org/10.1112/mtk.70002","url":null,"abstract":"<p>Let <span></span><math></math> and <span></span><math></math>. We prove that, for any <span></span><math></math> and <span></span><math></math> as <span></span><math></math>,\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860913","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 family of singular Brascamp–Lieb inequalities with dimension datum (1,2,2,1)
IF 0.8 3区 数学
Mathematika Pub Date : 2024-12-08 DOI: 10.1112/mtk.70003
Fred Yu-Hsiang Lin
{"title":"On the family of singular Brascamp–Lieb inequalities with dimension datum (1,2,2,1)","authors":"Fred Yu-Hsiang Lin","doi":"10.1112/mtk.70003","DOIUrl":"https://doi.org/10.1112/mtk.70003","url":null,"abstract":"<p>Motivated by the triangular Hilbert transform, we classify a certain family of singular Brascamp–Lieb forms which we associate with the dimension datum (1,2,2,1). We determine the exact range of Lebesgue exponents, for which one has singular Brascamp–Lieb inequalities within this family. The remaining observations concern counter examples to boundedness. We compare with a counter-example showing that the triangular Hilbert form does not satisfy singular Brascamp–Lieb bounds in the endpoints.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860288","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 index of equidimensional flag manifolds 等维旗流形的指数
IF 0.8 3区 数学
Mathematika Pub Date : 2024-11-20 DOI: 10.1112/mtk.70001
Samik Basu, Bikramjit Kundu
{"title":"The index of equidimensional flag manifolds","authors":"Samik Basu,&nbsp;Bikramjit Kundu","doi":"10.1112/mtk.70001","DOIUrl":"https://doi.org/10.1112/mtk.70001","url":null,"abstract":"<p>In this paper, we consider the flag manifold of <span></span><math></math> orthogonal subspaces of equal dimension that carries an action of the cyclic group of order <span></span><math></math>. We provide a complete calculation of the associated Fadell–Husseini index. This may be thought of as an odd primary version of the computations of Baralić, Blagojevic, Karasev, and Vucic, for the Grassmann manifold <span></span><math></math>. These results have geometric consequences for <span></span><math></math>-fold orthogonal shadows of a convex body.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707822","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
Effective upper bounds on the number of resonances in potential scattering 势散射共振数的有效上限
IF 0.8 3区 数学
Mathematika Pub Date : 2024-11-19 DOI: 10.1112/mtk.70000
Jean-Claude Cuenin
{"title":"Effective upper bounds on the number of resonances in potential scattering","authors":"Jean-Claude Cuenin","doi":"10.1112/mtk.70000","DOIUrl":"https://doi.org/10.1112/mtk.70000","url":null,"abstract":"<p>We prove upper bounds on the number of resonances and eigenvalues of Schrödinger operators <span></span><math></math> with complex-valued potentials, where <span></span><math></math> is odd. The novel feature of our upper bounds is that they are <i>effective</i>, in the sense that they only depend on an exponentially weighted norm of V. Our main focus is on potentials in the Lorentz space <span></span><math></math>, but we also obtain new results for compactly supported or pointwise decaying potentials. The main technical innovation, possibly of independent interest, are singular value estimates for Fourier-extension type operators. The obtained upper bounds not only recover several known results in a unified way, they also provide new bounds for potentials that are not amenable to previous methods.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707960","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
Twisted mixed moments of the Riemann zeta function 黎曼兹塔函数的扭曲混合矩
IF 0.8 3区 数学
Mathematika Pub Date : 2024-11-04 DOI: 10.1112/mtk.12284
Javier Pliego
{"title":"Twisted mixed moments of the Riemann zeta function","authors":"Javier Pliego","doi":"10.1112/mtk.12284","DOIUrl":"https://doi.org/10.1112/mtk.12284","url":null,"abstract":"<p>We analyse a collection of twisted mixed moments of the Riemann zeta function and establish the validity of asymptotic formulae comprising on some instances secondary terms of the shape <span></span><math></math> for a suitable constant <span></span><math></math> and a polynomial <span></span><math></math>. Such examinations are performed both unconditionally and under the assumption of a weaker version of the <span></span><math></math>-conjecture.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579670","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
Diophantine approximation by rational numbers of certain parity types 用某些奇偶类型的有理数进行二叉逼近
IF 0.8 3区 数学
Mathematika Pub Date : 2024-10-10 DOI: 10.1112/mtk.12285
Dong Han Kim, Seul Bee Lee, Lingmin Liao
{"title":"Diophantine approximation by rational numbers of certain parity types","authors":"Dong Han Kim,&nbsp;Seul Bee Lee,&nbsp;Lingmin Liao","doi":"10.1112/mtk.12285","DOIUrl":"https://doi.org/10.1112/mtk.12285","url":null,"abstract":"<p>For a given irrational number, we consider the properties of best rational approximations of given parities. There are three different kinds of rational numbers according to the parity of the numerator and denominator, say odd/odd, even/odd, and odd/even rational numbers. We study algorithms to find best approximations by rational numbers of given parities and compare these algorithms with continued fraction expansions.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12285","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429944","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
A discrete mean value of the Riemann zeta function 黎曼zeta函数的离散均值
IF 0.8 3区 数学
Mathematika Pub Date : 2024-09-30 DOI: 10.1112/mtk.12281
Kübra Benli, Ertan Elma, Nathan Ng
{"title":"A discrete mean value of the Riemann zeta function","authors":"Kübra Benli,&nbsp;Ertan Elma,&nbsp;Nathan Ng","doi":"10.1112/mtk.12281","DOIUrl":"https://doi.org/10.1112/mtk.12281","url":null,"abstract":"<p>In this work, we estimate the sum\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12281","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142360033","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 local solubility for homogeneous polynomials with random coefficients over thin sets 薄集上具有随机系数的同次多项式的局部溶解度
IF 0.8 3区 数学
Mathematika Pub Date : 2024-09-30 DOI: 10.1112/mtk.12282
Heejong Lee, Seungsu Lee, Kiseok Yeon
{"title":"The local solubility for homogeneous polynomials with random coefficients over thin sets","authors":"Heejong Lee,&nbsp;Seungsu Lee,&nbsp;Kiseok Yeon","doi":"10.1112/mtk.12282","DOIUrl":"https://doi.org/10.1112/mtk.12282","url":null,"abstract":"<p>Let <span></span><math></math> and <span></span><math></math> be natural numbers greater or equal to 2. Let <span></span><math></math> be a homogeneous polynomial in <span></span><math></math> variables of degree <span></span><math></math> with integer coefficients <span></span><math></math>, where <span></span><math></math> denotes the inner product, and <span></span><math></math> denotes the Veronese embedding with <span></span><math></math>. Consider a variety <span></span><math></math> in <span></span><math></math>, defined by <span></span><math></math>. In this paper, we examine a set of integer vectors <span></span><math></math>, defined by\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142360018","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
Tiling with monochromatic bipartite graphs of bounded maximum degree 用有界最大度的单色双方形图进行平铺
IF 0.8 3区 数学
Mathematika Pub Date : 2024-09-26 DOI: 10.1112/mtk.12280
António Girão, Oliver Janzer
{"title":"Tiling with monochromatic bipartite graphs of bounded maximum degree","authors":"António Girão,&nbsp;Oliver Janzer","doi":"10.1112/mtk.12280","DOIUrl":"https://doi.org/10.1112/mtk.12280","url":null,"abstract":"<p>We prove that for any <span></span><math></math>, there exists a constant <span></span><math></math> such that the following is true. Let <span></span><math></math> be an infinite sequence of bipartite graphs such that <span></span><math></math> and <span></span><math></math> hold for all <span></span><math></math>. Then, in any <span></span><math></math>-edge-coloured complete graph <span></span><math></math>, there is a collection of at most <span></span><math></math> monochromatic subgraphs, each of which is isomorphic to an element of <span></span><math></math>, whose vertex sets partition <span></span><math></math>. This proves a conjecture of Corsten and Mendonça in a strong form and generalises results on the multi-colour Ramsey numbers of bounded-degree bipartite graphs. It also settles the bipartite case of a general conjecture of Grinshpun and Sárközy.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12280","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142324691","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
Poissonian pair correlation for higher dimensional real sequences 高维实序列的泊松对相关性
IF 0.8 3区 数学
Mathematika Pub Date : 2024-09-26 DOI: 10.1112/mtk.12283
Tanmoy Bera, Mithun Kumar Das, Anirban Mukhopadhyay
{"title":"Poissonian pair correlation for higher dimensional real sequences","authors":"Tanmoy Bera,&nbsp;Mithun Kumar Das,&nbsp;Anirban Mukhopadhyay","doi":"10.1112/mtk.12283","DOIUrl":"https://doi.org/10.1112/mtk.12283","url":null,"abstract":"<p>In this article, we examine the Poissonian pair correlation (PPC) statistic for higher dimensional real sequences. Specifically, we demonstrate that for <span></span><math></math>, almost all <span></span><math></math>, the sequence <span></span><math></math> in <span></span><math></math> has PPC conditionally on the additive energy bound of <span></span><math></math>. This bound is more relaxed compared to the additive energy bound for one dimension as discussed in [Aistleitner, El-Baz, and Munsch, Geom. Funct. Anal. <b>31</b> (2021), 483–512]. More generally, we derive the PPC for <span></span><math></math> for almost all <span></span><math></math>. As a consequence we establish the metric PPC for <span></span><math></math> provided that all of the <span></span><math></math> are greater than two.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12283","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142324692","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
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