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Fractal uncertainty principle for discrete Cantor sets with random alphabets 带随机字母的离散康托尔集合的分形不确定性原理
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-07-17 DOI: 10.4310/mrl.2023.v30.n6.a2
Suresh Eswarathasan, Xiaolong Han
{"title":"Fractal uncertainty principle for discrete Cantor sets with random alphabets","authors":"Suresh Eswarathasan, Xiaolong Han","doi":"10.4310/mrl.2023.v30.n6.a2","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n6.a2","url":null,"abstract":"In this paper, we investigate the fractal uncertainty principle (FUP) for discrete Cantor sets, which are determined by an alphabet from a base of digits. Consider the base of $M$ digits and the alphabets of cardinality $A$ such that all the corresponding Cantor sets have a fixed dimension $log A/log Min (0,2/3)$. We prove that the FUP with an improved exponent over Dyatlov-Jin $href{https://doi.org/10.48550/arXiv.2107.08276}{textrm{DJ-1}}$ holds for almost all alphabets, asymptotically as $Mtoinfty$. Our result provides the best possible exponent when the Cantor sets enjoy either the strongest Fourier decay assumption or strongest additive energy assumption. The proof is based on a concentration of measure phenomenon in the space of alphabets.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744903","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
On radical filtrations of parabolic Verma modules 论抛物线维尔马模块的根滤波
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-05-14 DOI: 10.4310/mrl.2023.v30.n5.a7
Jun Hu, Wei Xiao
{"title":"On radical filtrations of parabolic Verma modules","authors":"Jun Hu, Wei Xiao","doi":"10.4310/mrl.2023.v30.n5.a7","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n5.a7","url":null,"abstract":"In this paper we give a sum formula for the radical filtration of parabolic Verma modules in any (possibly singular) blocks of parabolic BGG category. It can be viewed as a generalization of the Jantzen sum formula for Verma modules in the usual BGG category $mathcal{O}$. The proof makes use of the graded version of parabolic BGG category. Explicit formulae for the graded decomposition numbers and inverse graded decomposition numbers of parabolic Verma modules in any (possibly singular) integral blocks of the parabolic BGG category are also given in terms of the Kazhdan–Lusztig polynomials.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941577","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
$H^s$ bounds for the derivative nonlinear Schrödinger equation 导数非线性薛定谔方程的 $H^s$ 边界
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-05-14 DOI: 10.4310/mrl.2023.v30.n5.a1
Hajer Bahouri, Trevor M. Leslie, Galina Perelman
{"title":"$H^s$ bounds for the derivative nonlinear Schrödinger equation","authors":"Hajer Bahouri, Trevor M. Leslie, Galina Perelman","doi":"10.4310/mrl.2023.v30.n5.a1","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n5.a1","url":null,"abstract":"We study the derivative nonlinear Schrödinger equation on the real line and obtain global-in-time bounds on high order Sobolev norms.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941462","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
Finiteness of non-constant maps over a number field 数域上非常数映射的有限性
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-05-14 DOI: 10.4310/mrl.2023.v30.n5.a9
Ariyan Javanpeykar
{"title":"Finiteness of non-constant maps over a number field","authors":"Ariyan Javanpeykar","doi":"10.4310/mrl.2023.v30.n5.a9","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n5.a9","url":null,"abstract":"Motivated by the intermediate Lang conjectures on hyperbolicity and rational points, we prove new finiteness results for non-constant morphisms from a fixed variety to a fixed variety defined over a number field by applying Faltings’s finiteness results to moduli spaces of maps.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941585","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
A note on five dimensional kissing arrangements 关于五维吻合安排的说明
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-05-14 DOI: 10.4310/mrl.2023.v30.n5.a13
Ferenc Szöllősi
{"title":"A note on five dimensional kissing arrangements","authors":"Ferenc Szöllősi","doi":"10.4310/mrl.2023.v30.n5.a13","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n5.a13","url":null,"abstract":"The kissing number $tau (d)$ is the maximum number of pairwise non-overlapping unit spheres each touching a central unit sphere in the $d$-dimensional Euclidean space. In this note we report on how we discovered a new, previously unknown arrangement of 40 unit spheres in dimension $5$. Our arrangement saturates the best known lower bound on $tau (5)$, and refutes a ‘belief’ of Cohn–Jiao–Kumar–Torquato.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941576","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
Deformations of $log$ Calabi–Yau pairs can be obstructed $log$ Calabi-Yau 对的变形可能受阻
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-05-14 DOI: 10.4310/mrl.2023.v30.n5.a3
Simon Felten, Andrea Petracci, Sharon Robins
{"title":"Deformations of $log$ Calabi–Yau pairs can be obstructed","authors":"Simon Felten, Andrea Petracci, Sharon Robins","doi":"10.4310/mrl.2023.v30.n5.a3","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n5.a3","url":null,"abstract":"We exhibit examples of pairs $(X,D)$ where $X$ is a smooth projective variety and $D$ is an anticanonical reduced simple normal crossing divisor such that the deformations of $(X,D)$ are obstructed. These examples are constructed via toric geometry.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941580","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
Partial data inverse problems for nonlinear magnetic Schrödinger equations 非线性磁性薛定谔方程的部分数据逆问题
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-05-14 DOI: 10.4310/mrl.2023.v30.n5.a10
Ru-Yu Lai, Ting Zhou
{"title":"Partial data inverse problems for nonlinear magnetic Schrödinger equations","authors":"Ru-Yu Lai, Ting Zhou","doi":"10.4310/mrl.2023.v30.n5.a10","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n5.a10","url":null,"abstract":"We prove that the knowledge of the Dirichlet-to-Neumann map, measured on a part of the boundary of a bounded domain in $mathbb{R}^n , n geq 2$, can uniquely determine, in a nonlinear magnetic Schrödinger equation, the vector-valued magnetic potential and the scalar electric potential, both being nonlinear in the solution.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941504","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
Improved discrete restriction for the parabola 改进的抛物线离散限制
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-05-14 DOI: 10.4310/mrl.2023.v30.n5.a4
Shaoming Guo, Zane Kun Li, Po-Lam Yung
{"title":"Improved discrete restriction for the parabola","authors":"Shaoming Guo, Zane Kun Li, Po-Lam Yung","doi":"10.4310/mrl.2023.v30.n5.a4","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n5.a4","url":null,"abstract":"Using ideas from $href{https://doi.org/10.4171/jems/1295}{[7]}$ and working over $mathbb{Q}_p$, we show that the discrete restriction constant for the parabola is $O_varepsilon ((log M)^{2+varepsilon})$.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941574","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
On certain extensions of vector bundles in $p$-adic geometry 论 p$-adic 几何中向量束的某些扩展
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-05-14 DOI: 10.4310/mrl.2023.v30.n5.a6
Serin Hong
{"title":"On certain extensions of vector bundles in $p$-adic geometry","authors":"Serin Hong","doi":"10.4310/mrl.2023.v30.n5.a6","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n5.a6","url":null,"abstract":"Given two arbitrary vector bundles on the Fargues–Fontaine curve, we give an explicit criterion in terms of Harder–Narasimhan polygons on whether they realize a semistable vector bundle as their extensions. Our argument is largely combinatorial and builds upon the dimension analysis of certain moduli spaces of bundle maps developed in $href{https://doi.org/10.1017/S1474748020000183}{[1]}$.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941813","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
Modular forms, deformation of punctured spheres, and extensions of symmetric tensor representations 模块形式、穿刺球变形和对称张量表示的扩展
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-05-14 DOI: 10.4310/mrl.2023.v30.n5.a2
Gabriele Bogo
{"title":"Modular forms, deformation of punctured spheres, and extensions of symmetric tensor representations","authors":"Gabriele Bogo","doi":"10.4310/mrl.2023.v30.n5.a2","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n5.a2","url":null,"abstract":"Let $X = mathbb{H}/Gamma$ be an $n$-punctured sphere, $n gt 3$. We introduce and study $n-3$ deformation operators on the space of modular forms $M_ast (Gamma)$ based on the classical theory of uniformizing differential equations and accessory parameters. When restricting to modular functions, we recover a construction in Teichmüller theory related to the deformation of the complex structure of $X$. We describe the deformation operators in terms of derivations with respect to Eichler integrals of weight-four cusp forms, and in terms of vector-valued modular forms attached to extensions of symmetric tensor representations.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941477","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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