Advances in Mathematics最新文献_第10页

Theta liftings for (GLn,GLn) type dual pairs of loop groups （GLn,GLn）型对偶环群的θ升力

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-06-27 DOI: 10.1016/j.aim.2025.110417

Yanze Chen , Yongchang Zhu

引用次数: 0

The Chow ring of the universal Picard stack over the hyperelliptic locus 超椭圆轨迹上的泛Picard叠的Chow环

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-06-27 DOI: 10.1016/j.aim.2025.110412

Hannah Larson

引用次数: 0

Intersection probabilities for flats in hyperbolic space 双曲空间中平面的相交概率

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-06-27 DOI: 10.1016/j.aim.2025.110415

Ercan Sönmez, Panagiotis Spanos, Christoph Thäle

{"title":"Intersection probabilities for flats in hyperbolic space","authors":"Ercan Sönmez, Panagiotis Spanos, Christoph Thäle","doi":"10.1016/j.aim.2025.110415","DOIUrl":"10.1016/j.aim.2025.110415","url":null,"abstract":"<div><div>Consider the d-dimensional hyperbolic space <math><msubsup><mrow><mi>M</mi></mrow><mrow><mi>K</mi></mrow><mrow><mi>d</mi></mrow></msubsup></math> of constant curvature <math><mi>K</mi><mo><</mo><mn>0</mn></math> and fix a point o playing the role of an origin. Let L be a uniform random q-dimensional totally geodesic submanifold (called q-flat) in <math><msubsup><mrow><mi>M</mi></mrow><mrow><mi>K</mi></mrow><mrow><mi>d</mi></mrow></msubsup></math> passing through o and, independently of L, let E be a random <math><mo>(</mo><mi>d</mi><mo>−</mo><mi>q</mi><mo>+</mo><mi>γ</mi><mo>)</mo></math>-flat in <math><msubsup><mrow><mi>M</mi></mrow><mrow><mi>K</mi></mrow><mrow><mi>d</mi></mrow></msubsup></math> which is uniformly distributed in the set of all <math><mo>(</mo><mi>d</mi><mo>−</mo><mi>q</mi><mo>+</mo><mi>γ</mi><mo>)</mo></math>-flats intersecting a hyperbolic ball of radius <math><mi>u</mi><mo>></mo><mn>0</mn></math> around o. We are interested in the distribution of the random γ-flat arising as the intersection of E with L. In contrast to the Euclidean case, the intersection <math><mi>E</mi><mo>∩</mo><mi>L</mi></math> can be empty with strictly positive probability. We determine this probability and the full distribution of <math><mi>E</mi><mo>∩</mo><mi>L</mi></math>. Thereby, we elucidate crucial differences to the Euclidean case. Moreover, we study the limiting behavior as <math><mi>d</mi><mo>↑</mo><mo>∞</mo></math> and also <math><mi>K</mi><mo>↑</mo><mn>0</mn></math>. Thereby we obtain a phase transition with three different phases which we completely characterize, including a critical phase with distinctive behavior and a phase recovering the Euclidean results. In the background are methods from hyperbolic integral geometry.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"479 ","pages":"Article 110415"},"PeriodicalIF":1.5,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Riesz-type calculus for Lorentz-Morrey spaces Lorentz-Morrey空间的riesz型微积分

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-06-27 DOI: 10.1016/j.aim.2025.110414

Liguang Liu , Jie Xiao

引用次数: 0

C1,1 regularity for principal-agent problems 委托代理问题的正则性

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-06-25 DOI: 10.1016/j.aim.2025.110396

Robert J. McCann , Cale Rankin , Kelvin Shuangjian Zhang

引用次数: 0

Quantitative Runge type approximation theorems for zero solutions of certain partial differential operators 若干偏微分算子零解的定量Runge型逼近定理

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-06-25 DOI: 10.1016/j.aim.2025.110413

A. Debrouwere , T. Kalmes

引用次数: 0

The explicit hypergeometric-modularity method I 显式超几何模块化方法1

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-06-20 DOI: 10.1016/j.aim.2025.110411

Michael Allen , Brian Grove , Ling Long, Fang-Ting Tu

{"title":"The explicit hypergeometric-modularity method I","authors":"Michael Allen , Brian Grove , Ling Long, Fang-Ting Tu","doi":"10.1016/j.aim.2025.110411","DOIUrl":"10.1016/j.aim.2025.110411","url":null,"abstract":"<div><div>The theories of hypergeometric functions and modular forms are highly intertwined. For example, particular values of truncated hypergeometric functions and hypergeometric character sums are often congruent or equal to Fourier coefficients of modular forms. In this series of papers, we develop and explore an explicit “Hypergeometric-Modularity” method for associating a modular form to a given hypergeometric datum. In particular, for certain length three and four hypergeometric data we give an explicit method for finding a modular form f such that the corresponding hypergeometric Galois representation has a subrepresentation isomorphic to the Deligne representation of f. Our method utilizes Ramanujan's theory of elliptic functions to alternative bases, commutative formal group laws, and supercongruences. As a byproduct, we give a collection of eta quotients with multiplicative coefficients constructed from hypergeometric functions. In the second paper, we discuss a number of applications, including explicit connections between hypergeometric values and periods of these explicit eta quotients as well as evaluation formulae for certain special L-values.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"478 ","pages":"Article 110411"},"PeriodicalIF":1.5,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Typicality of operators on Fréchet algebras admitting a hypercyclic algebra 具有超循环代数的fr<s:1>代数上算子的典型性

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-06-18 DOI: 10.1016/j.aim.2025.110406

William Alexandre , Clifford Gilmore , Sophie Grivaux

{"title":"Typicality of operators on Fréchet algebras admitting a hypercyclic algebra","authors":"William Alexandre , Clifford Gilmore , Sophie Grivaux","doi":"10.1016/j.aim.2025.110406","DOIUrl":"10.1016/j.aim.2025.110406","url":null,"abstract":"<div><div>This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fréchet algebras, endowed with the topology of pointwise convergence. Our main results show that within natural Polish spaces of continuous operators acting on the algebra <math><mi>H</mi><mo>(</mo><mi>C</mi><mo>)</mo></math> of entire functions on <math><mi>C</mi></math>, a typical operator supports a hypercyclic algebra. We also investigate the case of the complex Fréchet algebras <math><mi>X</mi><mo>=</mo><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo></math>, <math><mn>1</mn><mo>≤</mo><mi>p</mi><mo><</mo><mo>+</mo><mo>∞</mo></math>, or <math><mi>X</mi><mo>=</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo></math> endowed with the coordinatewise product, and show that whenever <math><mi>M</mi><mo>></mo><mn>1</mn></math>, a typical operator on X of norm less than or equal to M admits a hypercyclic algebra.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"478 ","pages":"Article 110406"},"PeriodicalIF":1.5,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Sharp estimates for the Cramér transform of log-concave measures and geometric applications 对数凹测度的cramsamr变换的尖锐估计及其几何应用

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-06-18 DOI: 10.1016/j.aim.2025.110407

Silouanos Brazitikos , Giorgos Chasapis

引用次数: 0

CMC hypersurface with finite index in hyperbolic space H4 双曲空间H4中有限指数的CMC超曲面

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-06-18 DOI: 10.1016/j.aim.2025.110408

Han Hong

引用次数: 0