发布求助
文献互助 智能选刊 最新文献

arXiv - MATH - Number Theory最新文献

筛选
英文 中文
A weighted vertical Sato-Tate law for Maaß forms on $rm{GSp}_4$ $rm{GSp}_4$上Maaß形式的加权垂直萨托-塔特定律
arXiv - MATH - Number Theory Pub Date : 2024-09-09 DOI: arxiv-2409.06027
Félicien Comtat
{"title":"A weighted vertical Sato-Tate law for Maaß forms on $rm{GSp}_4$","authors":"Félicien Comtat","doi":"arxiv-2409.06027","DOIUrl":"https://doi.org/arxiv-2409.06027","url":null,"abstract":"We prove a weighted Sato-Tate law for the Satake parameters of automorphic\u0000forms on $rm{GSp}_4$ with respect to a fairly general congruence subgroup $H$\u0000whose level tends to infinity. When the level is squarefree we refine our\u0000result to the cuspidal spectrum. The ingredients are the $rm{GSp}_4$ Kuznetsov\u0000formula and the explicit calculation of local integrals involved in the\u0000Whittaker coefficients of $rm{GSp}_4$ Eisenstein series. We also discuss how\u0000the problem of bounding the continuous spectrum in the level aspect naturally\u0000leads to some combinatorial questions involving the double cosets in $P\u0000backslash G / H$, for each parabolic subgroup $P$.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Low Discrepancy Digital Kronecker-Van der Corput Sequences 低差分数字克罗内克-范德科普特序列
arXiv - MATH - Number Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05469
Steven Robertson
{"title":"Low Discrepancy Digital Kronecker-Van der Corput Sequences","authors":"Steven Robertson","doi":"arxiv-2409.05469","DOIUrl":"https://doi.org/arxiv-2409.05469","url":null,"abstract":"The discrepancy of a sequence measures how quickly it approaches a uniform\u0000distribution. Given a natural number $d$, any collection of one-dimensional\u0000so-called low discrepancy sequences $left{S_i:1le i le dright}$ can be\u0000concatenated to create a $d$-dimensional $textit{hybrid sequence}$\u0000$(S_1,dots,S_d)$. Since their introduction by Spanier in 1995, many\u0000connections between the discrepancy of a hybrid sequence and the discrepancy of\u0000its component sequences have been discovered. However, a proof that a hybrid\u0000sequence is capable of being low discrepancy has remained elusive. This paper\u0000remedies this by providing an explicit connection between Diophantine\u0000approximation over function fields and two dimensional low discrepancy hybrid\u0000sequences. Specifically, let $mathbb{F}_q$ be the finite field of cardinality $q$. It\u0000is shown that some real numbered hybrid sequence\u0000$mathbf{H}(Theta(t),P(t)):=textbf{H}(Theta,P)$ built from the digital\u0000Kronecker sequence associated to a Laurent series\u0000$Theta(t)inmathbb{F}_q((t^{-1}))$ and the digital Van der Corput sequence\u0000associated to an irreducible polynomial $P(t)inmathbb{F}_q[t]$ meets the\u0000above property. More precisely, if $Theta(t)$ is a counterexample to the so\u0000called $t$$textit{-adic Littlewood Conjecture}$ ($t$-$LC$), then another\u0000Laurent series $Phi(t)inmathbb{F}_q((t^{-1}))$ induced from $Theta(t)$ and\u0000$P(t)$ can be constructed so that $mathbf{H}(Phi,P)$ is low discrepancy. Such\u0000counterexamples to $t$-$LC$ are known over a number of finite fields by, on the\u0000one hand, Adiceam, Nesharim and Lunnon, and on the other, by Garrett and the\u0000author.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniform Discreteness of Discrete Orbits of Non-Uniform Lattices in $SL_2(mathbb{R})$ $SL_2(mathbb{R})$中非均匀网格的离散轨道的均匀不严密性
arXiv - MATH - Number Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05935
Sahar Bashan
{"title":"Uniform Discreteness of Discrete Orbits of Non-Uniform Lattices in $SL_2(mathbb{R})$","authors":"Sahar Bashan","doi":"arxiv-2409.05935","DOIUrl":"https://doi.org/arxiv-2409.05935","url":null,"abstract":"We study the property of uniform discreteness within discrete orbits of\u0000non-uniform lattices in $SL_2(mathbb{R})$, acting on $mathbb{R}^2$ by linear\u0000transformations. We provide a new proof of the conditions under which the orbit\u0000of a non-uniform lattice in $SL_2(mathbb{R})$ is uniformly discrete, by using\u0000Diophantine properties. Our results include a detailed analysis of the\u0000asymptotic behavior of the error terms. Focusing on a specific group $Gamma$\u0000and a discrete orbit of it, $S$, the main result of this paper is that for any\u0000$epsilon>0$, three points in $S$ can be found on a horizontal line within\u0000distance $epsilon$ of each other. This gives a partial result toward a\u0000conjecture of Leli`evre. The set $S$ and group $Gamma$ are respectively the\u0000set of long cylinder holonomy vectors, and Veech group, of the \"golden L\"\u0000translation surface.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ergodicity and Algebraticity of the Fast and Slow Triangle Maps 快慢三角映射的遍历性和代数性
arXiv - MATH - Number Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05822
Thomas Garrity, Jacob Lehmann Duke
{"title":"Ergodicity and Algebraticity of the Fast and Slow Triangle Maps","authors":"Thomas Garrity, Jacob Lehmann Duke","doi":"arxiv-2409.05822","DOIUrl":"https://doi.org/arxiv-2409.05822","url":null,"abstract":"Our goal is to show that both the fast and slow versions of the triangle map\u0000(a type of multi-dimensional continued fraction algorithm) in dimension $n$ are\u0000ergodic, resolving a conjecture of Messaoudi, Noguiera and Schweiger. This\u0000particular type of higher dimensional multi-dimensional continued fraction\u0000algorithm has recently been linked to the study of partition numbers, with the\u0000result that the underlying dynamics has combinatorial implications.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotics for smooth numbers in short intervals 短区间平稳数的渐近线
arXiv - MATH - Number Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05761
Khalid Younis
{"title":"Asymptotics for smooth numbers in short intervals","authors":"Khalid Younis","doi":"arxiv-2409.05761","DOIUrl":"https://doi.org/arxiv-2409.05761","url":null,"abstract":"A number is said to be $y$-smooth if all of its prime factors are less than\u0000or equal to $y.$ For all $17/30<thetaleq 1,$ we show that the density of\u0000$y$-smooth numbers in the short interval $[x,x+x^{theta}]$ is asymptotically\u0000equal to the density of $y$-smooth numbers in the long interval $[1,x],$ for\u0000all $y geq exp((log x)^{2/3+varepsilon}).$ Assuming the Riemann Hypothesis,\u0000we also prove that for all $1/2<thetaleq 1$ there exists a large constant $K$\u0000such that the expected asymptotic result holds for $ygeq (log x)^{K}.$ Our approach is to count smooth numbers using a Perron integral, shift this\u0000to a particular contour left of the saddle point, and employ a zero-density\u0000estimate of the Riemann zeta function.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Database of Continued Fractions of Polynomial Type 多项式类型的连续分数数据库
arXiv - MATH - Number Theory Pub Date : 2024-09-09 DOI: arxiv-2409.06086
Henri Cohen
{"title":"A Database of Continued Fractions of Polynomial Type","authors":"Henri Cohen","doi":"arxiv-2409.06086","DOIUrl":"https://doi.org/arxiv-2409.06086","url":null,"abstract":"We describe a database of 1307 continued fractions with polynomial\u0000coefficients, of which more than 1000 are new, both for interesting constants\u0000and for transcendental functions, and provide the database inside the TeX\u0000source of the paper. Look in particular at the section ``Table of Contents''.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algorithms for complementary sequences 互补序列算法
arXiv - MATH - Number Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05844
Chai Wah Wu
{"title":"Algorithms for complementary sequences","authors":"Chai Wah Wu","doi":"arxiv-2409.05844","DOIUrl":"https://doi.org/arxiv-2409.05844","url":null,"abstract":"Finding the n-th positive square number is easy, as it is simply $n^2$. But\u0000how do we find the complementary sequence, i.e. the n-th positive nonsquare\u0000number? For this case there is an explicit formula. However, for general\u0000constraints on a number, this is harder to find. In this brief note, we study\u0000how to compute the n-th integer that does (or does not) satisfy a certain\u0000condition. In particular, we consider it as a fixed point problem, relate it to\u0000the iterative method of Lambek and Moser, study a bisection approach to this\u0000problem and provide a new formula for the n-th non-k-th power.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Large degree primitive points on curves 曲线上的大度原始点
arXiv - MATH - Number Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05796
Maarten Derickx
{"title":"Large degree primitive points on curves","authors":"Maarten Derickx","doi":"arxiv-2409.05796","DOIUrl":"https://doi.org/arxiv-2409.05796","url":null,"abstract":"A number field $K$ is called primitive if $mathbb Q$ and $K$ are the only\u0000subfields of $K$. Let $X$ be a nice curve over $mathbb Q$ of genus $g$. A\u0000point $P$ of degree $d$ on $X$ is called primitive if the field of definition\u0000$mathbb Q(P)$ of the point is primitive. In this short note we prove that if\u0000$X$ has a divisor of degree $d> 2g$, then $X$ has infinitely many primitive\u0000points of degree $d$. This complements the results of Khawaja and Siksek that\u0000show that points of low degree are not primitive under certain conditions.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounded distance equivalence of cut-and-project sets and equidecomposability 切分与投影集合的有界距离等价性和可等价分解性
arXiv - MATH - Number Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05450
Sigrid Grepstad
{"title":"Bounded distance equivalence of cut-and-project sets and equidecomposability","authors":"Sigrid Grepstad","doi":"arxiv-2409.05450","DOIUrl":"https://doi.org/arxiv-2409.05450","url":null,"abstract":"We show that given a lattice $Gamma subset mathbb{R}^m times\u0000mathbb{R}^n$, and projections $p_1$ and $p_2$ onto $mathbb{R}^m$ and\u0000$mathbb{R}^n$ respectively, cut-and-project sets obtained using Jordan\u0000measurable windows $W$ and $W'$ in $mathbb{R}^n$ of equal measure are bounded\u0000distance equivalent only if $W$ and $W'$ are equidecomposable by translations\u0000in $p_2(Gamma)$. As a consequence, we obtain an explicit description of the\u0000bounded distance equivalence classes in the hulls of simple quasicrystals.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Zeta functions enumerating subforms of quadratic forms 枚举二次函数子形式的 Zeta 函数
arXiv - MATH - Number Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05625
Daejun Kim, Seok Hyeong Lee, Seungjai Lee
{"title":"Zeta functions enumerating subforms of quadratic forms","authors":"Daejun Kim, Seok Hyeong Lee, Seungjai Lee","doi":"arxiv-2409.05625","DOIUrl":"https://doi.org/arxiv-2409.05625","url":null,"abstract":"In this paper, we introduce and study the Dirichlet series enumerating\u0000(proper) equivalence classes of full rank subforms/sublattices of a given\u0000quadratic form/lattice, focusing on the positive definite binary case. We\u0000obtain formulas linking this Dirichlet series with Dirichlet series counting\u0000ideal classes of the imaginary quadratic field associated with the quadratic\u0000form. Utilizing the result, we provide explicit formulas of the Dirichlet\u0000series for several lattices, including square lattice and hexagonal lattice.\u0000Moreover, we investigate some analytic properties of this Dirichlet series.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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