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A Weyl equidistribution theorem over function fields 函数域上的Weyl等分布定理
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-28 DOI: 10.1007/s00013-025-02215-w
Ethan Ackelsberg
{"title":"A Weyl equidistribution theorem over function fields","authors":"Ethan Ackelsberg","doi":"10.1007/s00013-025-02215-w","DOIUrl":"10.1007/s00013-025-02215-w","url":null,"abstract":"<div><p>A classical theorem of Weyl states that any polynomial with an irrational coefficient other than the constant term is uniformly distributed mod 1. We prove a new function field analogue of this statement, confirming a conjecture of Lê, Liu, and Wooley.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"257 - 266"},"PeriodicalIF":0.5,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02215-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 note on the Cramér–Granville model 关于cramsamr - granville模型的注释
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-27 DOI: 10.1007/s00013-025-02214-x
Christian Táfula
{"title":"A note on the Cramér–Granville model","authors":"Christian Táfula","doi":"10.1007/s00013-025-02214-x","DOIUrl":"10.1007/s00013-025-02214-x","url":null,"abstract":"<div><p>We show the existence of a set <span>(Asubseteq mathbb {Z}_{ge 2})</span> satisfying the estimates of the Bateman–Horn conjecture, Goldbach’s conjecture, and also </p><div><div><span>$$begin{aligned} #{ple x text { prime} ~|~ pin A} gg x(log log x)/(log x)^2. end{aligned}$$</span></div></div></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"275 - 283"},"PeriodicalIF":0.5,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02214-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 derived Lie algebras 关于派生李代数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-24 DOI: 10.1007/s00013-025-02206-x
Salvatore Siciliano, David A. Towers
{"title":"On derived Lie algebras","authors":"Salvatore Siciliano,&nbsp;David A. Towers","doi":"10.1007/s00013-025-02206-x","DOIUrl":"10.1007/s00013-025-02206-x","url":null,"abstract":"<div><p>In this paper, we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the corresponding problem for groups.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"139 - 151"},"PeriodicalIF":0.5,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02206-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
When is the elementary operator of length one an n-isometry? 什么时候长度为1的初等算子是n等距的？
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-21 DOI: 10.1007/s00013-025-02217-8
Mohamed Amine Aouichaoui
{"title":"When is the elementary operator of length one an n-isometry?","authors":"Mohamed Amine Aouichaoui","doi":"10.1007/s00013-025-02217-8","DOIUrl":"10.1007/s00013-025-02217-8","url":null,"abstract":"<div><p>We study <i>n</i>-isometric elementary operators of length one, highlighting the special case <span>(n=1)</span>, which is fundamental due to the importance and practical relevance of classical isometries. In this case, we provide two proofs: one based on norm arguments and the other using an identification with tensor products and standard factorization properties. For arbitrary <i>n</i>, we furnish a direct proof of a result by Caixing Gu on <i>n</i>-isometric elementary operators of length one, relying solely on an antiunitary cosimilarity and a single lemma, and thereby eschewing the auxiliary arguments of the original work.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"295 - 303"},"PeriodicalIF":0.5,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Loop space blow-up and scale calculus 循环空间放大和尺度演算
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-16 DOI: 10.1007/s00013-025-02211-0
Urs Frauenfelder, Joa Weber
{"title":"Loop space blow-up and scale calculus","authors":"Urs Frauenfelder,&nbsp;Joa Weber","doi":"10.1007/s00013-025-02211-0","DOIUrl":"10.1007/s00013-025-02211-0","url":null,"abstract":"<div><p>In this note, we show that the Barutello–Ortega–Verzini regularization map is scale smooth.\u0000</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"335 - 342"},"PeriodicalIF":0.5,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02211-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147335710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 fundamental eigenvalue gap of Sturm–Liouville operators Sturm-Liouville算子的基本特征值间隙
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-08 DOI: 10.1007/s00013-025-02213-y
Mohammed Ahrami, Zakaria El Allali, Evans M. Harrell II
{"title":"On the fundamental eigenvalue gap of Sturm–Liouville operators","authors":"Mohammed Ahrami,&nbsp;Zakaria El Allali,&nbsp;Evans M. Harrell II","doi":"10.1007/s00013-025-02213-y","DOIUrl":"10.1007/s00013-025-02213-y","url":null,"abstract":"<div><p>We use methods of direct optimization as in El Allali and Harrell (Proc Am Math Soc 150:57–587, 2022) to characterize the minimizers of the fundamental gap of Sturm–Liouville operators on an interval, under the constraint that the potential is of single-well form and that the weight function is of single-barrier form, and under similar constraints expressed in terms of convexity.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"187 - 197"},"PeriodicalIF":0.5,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Double algebraic genericity of universal forward-only harmonic functions on trees in the general case 一般情况下树上泛正调和函数的二重代数泛型
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-08 DOI: 10.1007/s00013-025-02193-z
Christos Angelos Konidas, Vassili Nestoridis
{"title":"Double algebraic genericity of universal forward-only harmonic functions on trees in the general case","authors":"Christos Angelos Konidas,&nbsp;Vassili Nestoridis","doi":"10.1007/s00013-025-02193-z","DOIUrl":"10.1007/s00013-025-02193-z","url":null,"abstract":"<div><p>It has been shown that the set of universal functions on trees contains a linear subspace except zero, dense in the space of forward-only harmonic functions. In this paper, we show that the set of universal functions contains two linear subspaces except zero, dense in the space of forward-only harmonic functions that intersect only at zero. We work in the most general case that has been studied so far, letting our functions take values over a topological vector space.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"165 - 176"},"PeriodicalIF":0.5,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 radical of group rings 在基团环的根上
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-07 DOI: 10.1007/s00013-025-02208-9
F. E. A. Johnson
{"title":"On the radical of group rings","authors":"F. E. A. Johnson","doi":"10.1007/s00013-025-02208-9","DOIUrl":"10.1007/s00013-025-02208-9","url":null,"abstract":"<div><p>It is conjectured that, for any group <i>G</i>, the Jacobson radical <span>(J({mathbb {Z}}[G]))</span> of the integral group ring <span>({mathbb {Z}}[G])</span> is zero. This is known to be true when <i>G</i> is finite. Here we show it is true for a reasonably large class of infinite groups, including finitely generated linear groups and groups which satisfy Higman’s ‘two unique products’ condition.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"239 - 246"},"PeriodicalIF":0.5,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02208-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 extensions of principal series representations 关于主级数表示的扩展
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-06 DOI: 10.1007/s00013-025-02210-1
Gautam H. Borisagar, Asfak Soneji
{"title":"On extensions of principal series representations","authors":"Gautam H. Borisagar,&nbsp;Asfak Soneji","doi":"10.1007/s00013-025-02210-1","DOIUrl":"10.1007/s00013-025-02210-1","url":null,"abstract":"<div><p>We compute <span>(textrm{Ext}^{1}_B(chi _1,chi _2))</span> between two characters <span>(chi _1,chi _2)</span> of a Borel subgroup <i>B</i> of a split reductive group <i>G</i> over a finite field <span>(mathbb {F}_q,)</span> and make an application to the calculation of <span>(textrm{Ext}^1_G(pi _1,pi _2))</span> between principal series representations <span>(pi _1,pi _2)</span> of <span>(G(mathbb {F}_q))</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"121 - 126"},"PeriodicalIF":0.5,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Answer to a question of Hung and Tiep on conductors of cyclotomic integers 关于环切整数导体的Hung和Tiep问题的回答
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-06 DOI: 10.1007/s00013-025-02212-z
Christopher Herbig
{"title":"Answer to a question of Hung and Tiep on conductors of cyclotomic integers","authors":"Christopher Herbig","doi":"10.1007/s00013-025-02212-z","DOIUrl":"10.1007/s00013-025-02212-z","url":null,"abstract":"<div><p>In Question 5.2, Hung and Tiep (Eur J Math 9, 2023) asked the following: If <span>(alpha )</span> is a sum of <i>k</i> complex roots of unity and <span>(mathbb {Q}_{c(alpha )})</span> is the smallest cyclotomic field containing <span>(alpha )</span>, is it true that <span>(|mathbb {Q}_{c(alpha )}:mathbb {Q}(alpha )| le k)</span>? We answer this question in the negative, and in §4, we shall bound the growth of <span>(|mathbb {Q}_{c(alpha )}:mathbb {Q}(alpha )|)</span> as a function of <i>k</i> using known results on minimal vanishing sums.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"247 - 256"},"PeriodicalIF":0.5,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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