发布求助
文献互助 智能选刊 最新文献

International Mathematics Research Notices最新文献

筛选
英文 中文
Frobenius Distributions of Low Dimensional Abelian Varieties Over Finite Fields 有限域上低维阿贝尔变种的 Frobenius 分布
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-07-06 DOI: 10.1093/imrn/rnae148
Santiago Arango-Piñeros, Deewang Bhamidipati, Soumya Sankar
{"title":"Frobenius Distributions of Low Dimensional Abelian Varieties Over Finite Fields","authors":"Santiago Arango-Piñeros, Deewang Bhamidipati, Soumya Sankar","doi":"10.1093/imrn/rnae148","DOIUrl":"https://doi.org/10.1093/imrn/rnae148","url":null,"abstract":"Given a $g$-dimensional abelian variety $A$ over a finite field $mathbf{F}_{q}$, the Weil conjectures imply that the normalized Frobenius eigenvalues generate a multiplicative group of rank at most $g$. The Pontryagin dual of this group is a compact abelian Lie group that controls the distribution of high powers of the Frobenius endomorphism. This group, which we call the Serre–Frobenius group, encodes the possible multiplicative relations between the Frobenius eigenvalues. In this article, we classify all possible Serre–Frobenius groups that occur for $g le 3$. We also give a partial classification for simple ordinary abelian varieties of prime dimension $ggeq 3$.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Unique Continuation at Infinity: Carleman Estimates on General Warped Cylinders 无穷大时的独特延续：一般翘曲圆柱体上的卡勒曼估计值
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-07-04 DOI: 10.1093/imrn/rnae147
Nicolò De Ponti, Stefano Pigola, Giona Veronelli
{"title":"Unique Continuation at Infinity: Carleman Estimates on General Warped Cylinders","authors":"Nicolò De Ponti, Stefano Pigola, Giona Veronelli","doi":"10.1093/imrn/rnae147","DOIUrl":"https://doi.org/10.1093/imrn/rnae147","url":null,"abstract":"We obtain a vanishing result for solutions of the inequality $|Delta u| leq q_{1} |u| + q_{2} |nabla u|$ that decay to zero along a very general warped cylindrical end of a Riemannian manifold. The appropriate decay condition at infinity on $u$ is related to the behavior of the potential functions $q_{1}$ and $q_{2}$ and to the asymptotic geometry of the end. The main ingredient is a new Carleman estimate of independent interest. Geometric applications to conformal deformations and to minimal graphs are presented.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 a Goldbach-Type Problem for the Liouville Function 关于柳维尔函数的哥德巴赫问题
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-07-03 DOI: 10.1093/imrn/rnae149
Alexander P Mangerel
{"title":"On a Goldbach-Type Problem for the Liouville Function","authors":"Alexander P Mangerel","doi":"10.1093/imrn/rnae149","DOIUrl":"https://doi.org/10.1093/imrn/rnae149","url":null,"abstract":"Let $lambda $ denote the Liouville function. We show that for all $N geq 11$, the (non-trivial) convolution sum bound $$ begin{align*} & left|sum_{n < N} lambda(n) lambda(N-n)right| < N-1 end{align*} $$ holds. We also determine all $N$ for which no cancellation in the convolution sum occurs. This answers a question posed at the 2018 AIM workshop on Sarnak’s conjecture.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Cancellation for (G,n)-complexes and the Swan Finiteness Obstruction (G,n)复数的取消与天鹅有限性障碍
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-07-03 DOI: 10.1093/imrn/rnae141
John Nicholson
{"title":"Cancellation for (G,n)-complexes and the Swan Finiteness Obstruction","authors":"John Nicholson","doi":"10.1093/imrn/rnae141","DOIUrl":"https://doi.org/10.1093/imrn/rnae141","url":null,"abstract":"In previous work, we related homotopy types of finite $(G,n)$-complexes when $G$ has periodic cohomology to projective ${mathbb{Z}} G$-modules representing the Swan finiteness obstruction. We use this to determine when $X vee S^{n} simeq Y vee S^{n}$ implies $X simeq Y$ for finite $(G,n)$-complexes $X$ and $Y$, and give lower bounds on the number of homotopically distinct pairs when this fails. The proof involves constructing projective ${mathbb{Z}} G$-modules as lifts of locally free modules over orders in products of quaternion algebras, whose existence follows from the Eichler mass formula. In the case $n=2$, difficulties arise that lead to a new approach to finding a counterexample to Wall’s D2 problem.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
The Conformal Limit and Projective Structures 共形极限与投影结构
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-07-03 DOI: 10.1093/imrn/rnae142
Pedro M Silva, Peter B Gothen
{"title":"The Conformal Limit and Projective Structures","authors":"Pedro M Silva, Peter B Gothen","doi":"10.1093/imrn/rnae142","DOIUrl":"https://doi.org/10.1093/imrn/rnae142","url":null,"abstract":"The non-abelian Hodge correspondence maps a polystable $textrm{SL}(2, {mathbb{R}})$-Higgs bundle on a compact Riemann surface $X$ of genus $g geq 2$ to a connection that, in some cases, is the holonomy of a branched hyperbolic structure. Gaiotto’s conformal limit maps the same bundle to a partial oper, that is, to a connection whose holonomy is that of a branched complex projective structure compatible with $X$. In this article, we show how these are both instances of the same phenomenon: the family of connections appearing in the conformal limit can be understood as a family of complex projective structures, deforming the hyperbolic ones into the ones compatible with $X$. We also show that, for zero Toledo invariant, this deformation is optimal, inducing a geodesic on Teichmüller’s space.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Counting Arcs of the Same Type 计算相同类型的弧
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-06-27 DOI: 10.1093/imrn/rnae143
Marie Trin
{"title":"Counting Arcs of the Same Type","authors":"Marie Trin","doi":"10.1093/imrn/rnae143","DOIUrl":"https://doi.org/10.1093/imrn/rnae143","url":null,"abstract":"We prove a general counting result for arcs of the same type in compact surfaces. We also count infinite arcs in cusped surfaces and arcs in orbifolds. These theorems are derived from a result that ensures the convergence of certain measures on the space of geodesic currents.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Descent and Étale-Brauer Obstructions for 0-Cycles 0 循环的下降和埃塔勒-布劳尔障碍
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-06-27 DOI: 10.1093/imrn/rnae140
Francesca Balestrieri, Jennifer Berg
{"title":"Descent and Étale-Brauer Obstructions for 0-Cycles","authors":"Francesca Balestrieri, Jennifer Berg","doi":"10.1093/imrn/rnae140","DOIUrl":"https://doi.org/10.1093/imrn/rnae140","url":null,"abstract":"For 0-cycles on a variety over a number field, we define an analogue of the classical descent set for rational points. This leads to, among other things, a definition of the étale-Brauer obstruction set for 0-cycles. We show that all these constructions are compatible with Suslin’s singular homology of degree 0. We then transfer some tools and techniques used to study the arithmetic of rational points into the setting of 0-cycles. For example, we extend the strategy developed by Y. Liang, relating the arithmetic of rational points over finite extensions of the base field to that of 0-cycles, to torsors. We give applications of our results to study the arithmetic behaviour of 0-cycles for Enriques surfaces, torsors given by (twisted) Kummer varieties, universal torsors, and torsors under tori.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 the Local Fourier Uniformity Problem for Small Sets 论小集合的局部傅里叶均匀性问题
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-06-21 DOI: 10.1093/imrn/rnae134
Adam Kanigowski, Mariusz Lemańczyk, Florian K Richter, Joni Teräväinen
{"title":"On the Local Fourier Uniformity Problem for Small Sets","authors":"Adam Kanigowski, Mariusz Lemańczyk, Florian K Richter, Joni Teräväinen","doi":"10.1093/imrn/rnae134","DOIUrl":"https://doi.org/10.1093/imrn/rnae134","url":null,"abstract":"We consider vanishing properties of exponential sums of the Liouville function $boldsymbol{lambda }$ of the form $$ begin{align*} & lim_{Htoinfty}limsup_{Xtoinfty}frac{1}{log X}sum_{mleq X}frac{1}{m}sup_{alphain C}bigg|frac{1}{H}sum_{hleq H}boldsymbol{lambda}(m+h)e^{2pi ihalpha}bigg|=0, end{align*} $$ where $Csubset{{mathbb{T}}}$. The case $C={{mathbb{T}}}$ corresponds to the local $1$-Fourier uniformity conjecture of Tao, a central open problem in the study of multiplicative functions with far-reaching number-theoretic applications. We show that the above holds for any closed set $Csubset{{mathbb{T}}}$ of zero Lebesgue measure. Moreover, we prove that extending this to any set $C$ with non-empty interior is equivalent to the $C={{mathbb{T}}}$ case, which shows that our results are essentially optimal without resolving the full conjecture. We also consider higher-order variants. We prove that if the linear phase $e^{2pi ihalpha }$ is replaced by a polynomial phase $e^{2pi ih^{t}alpha }$ for $tgeq 2$ then the statement remains true for any set $C$ of upper box-counting dimension $< 1/t$. The statement also remains true if the supremum over linear phases is replaced with a supremum over all nilsequences coming form a compact countable ergodic subsets of any $t$-step nilpotent Lie group. Furthermore, we discuss the unweighted version of the local $1$-Fourier uniformity problem, showing its validity for a class of “rigid” sets (of full Hausdorff dimension) and proving a density result for all closed subsets of zero Lebesgue measure.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Real Roots of Hypergeometric Polynomials via Finite Free Convolution 通过有限自由卷积求超几何多项式的实根
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-06-21 DOI: 10.1093/imrn/rnae120
Andrei Martínez-Finkelshtein, Rafael Morales, Daniel Perales
{"title":"Real Roots of Hypergeometric Polynomials via Finite Free Convolution","authors":"Andrei Martínez-Finkelshtein, Rafael Morales, Daniel Perales","doi":"10.1093/imrn/rnae120","DOIUrl":"https://doi.org/10.1093/imrn/rnae120","url":null,"abstract":"We examine two binary operations on the set of algebraic polynomials, known as multiplicative and additive finite free convolutions, specifically in the context of hypergeometric polynomials. We show that the representation of a hypergeometric polynomial as a finite free convolution of more elementary blocks, combined with the preservation of the real zeros and interlacing by the free convolutions, is an effective tool that allows us to analyze when all roots of a specific hypergeometric polynomial are real. Moreover, the known limit behavior of finite free convolutions allows us to write the asymptotic zero distribution of some hypergeometric polynomials as free convolutions of Marchenko–Pastur, reciprocal Marchenko–Pastur, and free beta laws, which has an independent interest within free probability.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Polynomial Representations of the Witt Lie Algebra 维特列支代数的多项式表示
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-06-21 DOI: 10.1093/imrn/rnae139
Steven V Sam, Andrew Snowden, Philip Tosteson
{"title":"Polynomial Representations of the Witt Lie Algebra","authors":"Steven V Sam, Andrew Snowden, Philip Tosteson","doi":"10.1093/imrn/rnae139","DOIUrl":"https://doi.org/10.1093/imrn/rnae139","url":null,"abstract":"The Witt algebra ${mathfrak{W}}_{n}$ is the Lie algebra of all derivations of the $n$-variable polynomial ring $textbf{V}_{n}=textbf{C}[x_{1}, ldots , x_{n}]$ (or of algebraic vector fields on $textbf{A}^{n}$). A representation of ${mathfrak{W}}_{n}$ is polynomial if it arises as a subquotient of a sum of tensor powers of $textbf{V}_{n}$. Our main theorems assert that finitely generated polynomial representations of ${mathfrak{W}}_{n}$ are noetherian and have rational Hilbert series. A key intermediate result states polynomial representations of the infinite Witt algebra are equivalent to representations of $textbf{Fin}^{textrm{op}}$, where $textbf{Fin}$ is the category of finite sets. We also show that polynomial representations of ${mathfrak{W}}_{n}$ are equivalent to polynomial representations of the endomorphism monoid of $textbf{A}^{n}$. These equivalences are a special case of an operadic version of Schur–Weyl duality, which we establish.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信