发布求助
文献互助 智能选刊 最新文献

Mathematika最新文献

筛选
英文 中文
Asymptotic Fermat's last theorem for a family of equations of signature 符号方程组的渐近费马最后定理
IF 0.8 3区 数学
Mathematika Pub Date : 2024-08-29 DOI: 10.1112/mtk.12279
Pedro-José Cazorla García
{"title":"Asymptotic Fermat's last theorem for a family of equations of signature","authors":"Pedro-José Cazorla García","doi":"10.1112/mtk.12279","DOIUrl":"https://doi.org/10.1112/mtk.12279","url":null,"abstract":"<p>In this paper, we study the integer solutions of a family of Fermat-type equations of signature <span></span><math></math>, <span></span><math></math>. We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant <span></span><math></math> such that if <span></span><math></math>, there are no solutions <span></span><math></math> of the equation. Our methods use the modular method for Diophantine equations, along with level lowering and Galois theory.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12279","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142100080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 squarefree density of polynomials 关于多项式无平方密度的说明
IF 0.8 3区 数学
Mathematika Pub Date : 2024-08-26 DOI: 10.1112/mtk.12275
R. C. Vaughan, Yu. G. Zarhin
{"title":"A note on the squarefree density of polynomials","authors":"R. C. Vaughan,&nbsp;Yu. G. Zarhin","doi":"10.1112/mtk.12275","DOIUrl":"https://doi.org/10.1112/mtk.12275","url":null,"abstract":"<p>The conjectured squarefree density of an integral polynomial <span></span><math></math> in <span></span><math></math> variables is an Euler product <span></span><math></math> which can be considered as a product of local densities. We show that a necessary and sufficient condition for <span></span><math></math> to be 0 when <span></span><math></math> is a polynomial in <span></span><math></math> variables over the integers, is that either there is a prime <span></span><math></math> such that the values of <span></span><math></math> at all integer points are divisible by <span></span><math></math> or the polynomial is not squarefree as a polynomial. We also show that generally the upper squarefree density <span></span><math></math> satisfies <span></span><math></math>.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12275","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142077770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
The interplay between bounded ranks of tensors arising from partitions 分区引起的张量有界等级之间的相互作用
IF 0.8 3区 数学
Mathematika Pub Date : 2024-08-25 DOI: 10.1112/mtk.12277
Thomas Karam
{"title":"The interplay between bounded ranks of tensors arising from partitions","authors":"Thomas Karam","doi":"10.1112/mtk.12277","DOIUrl":"https://doi.org/10.1112/mtk.12277","url":null,"abstract":"<p>Let <span></span><math></math> be integers. Using a fragmentation technique, we characterise <span></span><math></math>-tuples <span></span><math></math> of non-empty families of partitions of <span></span><math></math> such that it suffices that an order-<span></span><math></math> tensor has bounded <span></span><math></math>-rank for each <span></span><math></math> for it to have bounded <span></span><math></math>-rank. On the way, we prove power lower bounds on suitable products of diagonal tensors, providing a qualitative answer to a question of Naslund.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142077971","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 Waring numbers of henselian rings 论恒星环的瓦林数
IF 0.8 3区 数学
Mathematika Pub Date : 2024-08-25 DOI: 10.1112/mtk.12276
Tomasz Kowalczyk, Piotr Miska
{"title":"On Waring numbers of henselian rings","authors":"Tomasz Kowalczyk,&nbsp;Piotr Miska","doi":"10.1112/mtk.12276","DOIUrl":"https://doi.org/10.1112/mtk.12276","url":null,"abstract":"<p>Let <span></span><math></math> be a positive integer. Let <span></span><math></math> be a henselian local ring with residue field <span></span><math></math> of <span></span><math></math>th level <span></span><math></math>. We give some upper and lower bounds for the <span></span><math></math>th Waring number <span></span><math></math> in terms of <span></span><math></math> and <span></span><math></math>. In large number of cases, we are able to compute <span></span><math></math>. Similar results for the <span></span><math></math>th Waring number of the total ring of fractions of <span></span><math></math> are obtained. We then provide applications. In particular, we compute <span></span><math></math> and <span></span><math></math> for <span></span><math></math> and any prime <span></span><math></math>.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142077970","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
An overdetermined problem related to the Finsler -Laplacian 与芬斯勒-拉普拉奇相关的超定问题
IF 0.8 3区 数学
Mathematika Pub Date : 2024-08-05 DOI: 10.1112/mtk.12267
Antonio Greco, Benyam Mebrate
{"title":"An overdetermined problem related to the Finsler -Laplacian","authors":"Antonio Greco,&nbsp;Benyam Mebrate","doi":"10.1112/mtk.12267","DOIUrl":"https://doi.org/10.1112/mtk.12267","url":null,"abstract":"<p>In this paper, we consider the Finsler <span></span><math></math>-Laplacian torsion equation. The domain of the problem is bounded by a conical surface supporting a Neumann-type condition, and an unknown surface supporting both a Dirichlet and a Neumann condition. The case when the cone coincides with the punctured space is included. We show that the existence of a weak solution implies that the unknown surface lies on the boundary of a Finsler-ball. Incidentally, some properties of the Finsler–Minkowski norms are proved here under mild smoothness assumptions.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12267","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141967317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Explicit continued fraction expansion of a rational root of over 有理根的显式续分数展开式
IF 0.8 3区 数学
Mathematika Pub Date : 2024-07-29 DOI: 10.1112/mtk.12271
Yann Bugeaud, Guo-Niu Han
{"title":"Explicit continued fraction expansion of a rational root of over","authors":"Yann Bugeaud,&nbsp;Guo-Niu Han","doi":"10.1112/mtk.12271","DOIUrl":"https://doi.org/10.1112/mtk.12271","url":null,"abstract":"<p>Let <span></span><math></math> be a prime number, <span></span><math></math> and <span></span><math></math> positive integers coprime with <span></span><math></math>. We provide the explicit continued fraction expansion of the <span></span><math></math>th root of <span></span><math></math> in the power series field <span></span><math></math>. We determine its irrationality exponent.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968311","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
The first and second moments for the length of the period of the continued fraction expansion for 的续分扩展周期长度的第一和第二矩
IF 0.8 3区 数学
Mathematika Pub Date : 2024-07-23 DOI: 10.1112/mtk.12273
Francesco Battistoni, Loïc Grenié, Giuseppe Molteni
{"title":"The first and second moments for the length of the period of the continued fraction expansion for","authors":"Francesco Battistoni,&nbsp;Loïc Grenié,&nbsp;Giuseppe Molteni","doi":"10.1112/mtk.12273","DOIUrl":"https://doi.org/10.1112/mtk.12273","url":null,"abstract":"<p>Let <span></span><math></math> be any positive and non-square integer. We prove an upper bound for the first two moments of the length <span></span><math></math> of the period of the continued fraction expansion for <span></span><math></math>. This allows to improve the existing results for the large deviations of <span></span><math></math>.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968078","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
Strong divisibility sequences and sieve methods 强可分性序列和筛分方法
IF 0.8 3区 数学
Mathematika Pub Date : 2024-07-23 DOI: 10.1112/mtk.12269
Tim Browning, Matteo Verzobio
{"title":"Strong divisibility sequences and sieve methods","authors":"Tim Browning,&nbsp;Matteo Verzobio","doi":"10.1112/mtk.12269","DOIUrl":"https://doi.org/10.1112/mtk.12269","url":null,"abstract":"<p>We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence that only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods. At the end of the paper, there is an appendix by Sandro Bettin on divisor closed sets that we use to study the density of prime terms that appear in strong divisibility sequences.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12269","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Correlations of the Riemann zeta function 黎曼zeta函数的相关性
IF 0.8 3区 数学
Mathematika Pub Date : 2024-07-20 DOI: 10.1112/mtk.12268
Michael J. Curran
{"title":"Correlations of the Riemann zeta function","authors":"Michael J. Curran","doi":"10.1112/mtk.12268","DOIUrl":"https://doi.org/10.1112/mtk.12268","url":null,"abstract":"<p>Assuming the Riemann hypothesis, we investigate the shifted moments of the zeta function\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12268","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 variance of the mean width of random polytopes circumscribed around a convex body 论环绕凸体的随机多边形平均宽度的方差
IF 0.8 3区 数学
Mathematika Pub Date : 2024-07-17 DOI: 10.1112/mtk.12266
Alexandra Bakó-Szabó, Ferenc Fodor
{"title":"On the variance of the mean width of random polytopes circumscribed around a convex body","authors":"Alexandra Bakó-Szabó,&nbsp;Ferenc Fodor","doi":"10.1112/mtk.12266","DOIUrl":"https://doi.org/10.1112/mtk.12266","url":null,"abstract":"<p>Let <span></span><math></math> be a convex body in <span></span><math></math> in which a ball rolls freely and which slides freely in a ball. Let <span></span><math></math> be the intersection of <span></span><math></math> i.i.d. random half-spaces containing <span></span><math></math> chosen according to a certain prescribed probability distribution. We prove an asymptotic upper bound on the variance of the mean width of <span></span><math></math> as <span></span><math></math>. We achieve this result by first proving an asymptotic upper bound on the variance of the weighted volume of random polytopes generated by <span></span><math></math> i.i.d. random points selected according to certain probability distributions, then, using polarity, we transfer this to the circumscribed model.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12266","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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：604180095
Book学术官方微信