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Mathematical Proceedings of the Cambridge Philosophical Society最新文献

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Compact groups with a set of positive Haar measure satisfying a nilpotent law 具有满足幂零定律的一组正哈尔测度的紧群
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2021-01-27 DOI: 10.1017/S0305004121000542
A. Abdollahi, Meisam Soleimani Malekan
{"title":"Compact groups with a set of positive Haar measure satisfying a nilpotent law","authors":"A. Abdollahi, Meisam Soleimani Malekan","doi":"10.1017/S0305004121000542","DOIUrl":"https://doi.org/10.1017/S0305004121000542","url":null,"abstract":"Abstract The following question is proposed by Martino, Tointon, Valiunas and Ventura in [4, question 1·20]: Let G be a compact group, and suppose that \u0000[mathcal{N}_k(G) = {(x_1,dots,x_{k+1}) in G^{k+1} ;|; [x_1,dots, x_{k+1}] = 1}]\u0000 has positive Haar measure in \u0000$G^{k+1}$\u0000 . Does G have an open k-step nilpotent subgroup? We give a positive answer for \u0000$k = 2$\u0000 .","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"4 1","pages":"329 - 332"},"PeriodicalIF":0.8,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74612612","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: 1
Number fields without universal quadratic forms of small rank exist in most degrees 没有小秩的普适二次型的数域在大多数度上都存在
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2021-01-25 DOI: 10.1017/S0305004122000214
Vítězslav Kala
{"title":"Number fields without universal quadratic forms of small rank exist in most degrees","authors":"Vítězslav Kala","doi":"10.1017/S0305004122000214","DOIUrl":"https://doi.org/10.1017/S0305004122000214","url":null,"abstract":"Abstract We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fields that require universal quadratic forms to have arbitrarily large rank.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"16 1","pages":"225 - 231"},"PeriodicalIF":0.8,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76019405","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: 7
Simultaneous p-adic Diophantine approximation 同时p进丢番图近似
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2021-01-13 DOI: 10.1017/S0305004122000470
V. Beresnevich, J. Levesley, Benjamin C. Ward
{"title":"Simultaneous p-adic Diophantine approximation","authors":"V. Beresnevich, J. Levesley, Benjamin C. Ward","doi":"10.1017/S0305004122000470","DOIUrl":"https://doi.org/10.1017/S0305004122000470","url":null,"abstract":"Abstract The aim of this paper is to develop the theory of weighted Diophantine approximation of rational numbers to p-adic numbers. Firstly, we establish complete analogues of Khintchine’s theorem, the Duffin–Schaeffer theorem and the Jarník–Besicovitch theorem for ‘weighted’ simultaneous Diophantine approximation in the p-adic case. Secondly, we obtain a lower bound for the Hausdorff dimension of weighted simultaneously approximable points lying on p-adic manifolds. This is valid for very general classes of curves and manifolds and have natural constraints on the exponents of approximation. The key tools we use in our proofs are the Mass Transference Principle, including its recent extension due to Wang and Wu in 2019, and a Zero-One law for weighted p-adic approximations established in this paper.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"8 1","pages":"13 - 50"},"PeriodicalIF":0.8,"publicationDate":"2021-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75032939","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: 7
PSP volume 170 issue 1 Cover and Back matter PSP第170卷第1期封面和封底
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2021-01-01 DOI: 10.1017/s0305004121000062
{"title":"PSP volume 170 issue 1 Cover and Back matter","authors":"","doi":"10.1017/s0305004121000062","DOIUrl":"https://doi.org/10.1017/s0305004121000062","url":null,"abstract":"","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"12 1","pages":"b1 - b2"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73178729","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
PSP volume 170 issue 1 Cover and Front matter PSP第170卷第1期封面和封面问题
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2021-01-01 DOI: 10.1017/s0305004121000050
{"title":"PSP volume 170 issue 1 Cover and Front matter","authors":"","doi":"10.1017/s0305004121000050","DOIUrl":"https://doi.org/10.1017/s0305004121000050","url":null,"abstract":"","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"222 1","pages":"f1 - f2"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76986597","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
Divisors computing minimal log discrepancies on lc surfaces 在lc表面上计算最小对数差异的除法
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2021-01-01 DOI: 10.1017/S0305004123000051
Jihao Liu, Lingyao Xie
{"title":"Divisors computing minimal log discrepancies on lc surfaces","authors":"Jihao Liu, Lingyao Xie","doi":"10.1017/S0305004123000051","DOIUrl":"https://doi.org/10.1017/S0305004123000051","url":null,"abstract":"Abstract Let \u0000$(Xni x,B)$\u0000 be an lc surface germ. If \u0000$Xni x$\u0000 is klt, we show that there exists a divisor computing the minimal log discrepancy of \u0000$(Xni x,B)$\u0000 that is a Kollár component of \u0000$Xni x$\u0000 . If \u0000$Bnot=0$\u0000 or \u0000$Xni x$\u0000 is not Du Val, we show that any divisor computing the minimal log discrepancy of \u0000$(Xni x,B)$\u0000 is a potential lc place of \u0000$Xni x$\u0000 . This extends a result of Blum and Kawakita who independently showed that any divisor computing the minimal log discrepancy on a smooth surface is a potential lc place.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"27 1","pages":"107 - 128"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82514515","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: 2
The Log Product Formula in Quantum K-theory 量子k理论中的对数积公式
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2020-12-17 DOI: 10.1017/S0305004123000063
You-Cheng Chou, Leo Herr, Yuan-Pin Lee
{"title":"The Log Product Formula in Quantum K-theory","authors":"You-Cheng Chou, Leo Herr, Yuan-Pin Lee","doi":"10.1017/S0305004123000063","DOIUrl":"https://doi.org/10.1017/S0305004123000063","url":null,"abstract":"Abstract We prove a formula expressing the K-theoretic log Gromov-Witten invariants of a product of log smooth varieties \u0000$V times W$\u0000 in terms of the invariants of V and W. The proof requires introducing log virtual fundamental classes in K-theory and verifying their various functorial properties. We introduce a log version of K-theory and prove the formula there as well.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"34 1","pages":"225 - 252"},"PeriodicalIF":0.8,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80045615","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: 8
Uniform bounds for norms of theta series and arithmetic applications 级数范数的统一界及其算术应用
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2020-12-08 DOI: 10.1017/S0305004122000081
F. Waibel
{"title":"Uniform bounds for norms of theta series and arithmetic applications","authors":"F. Waibel","doi":"10.1017/S0305004122000081","DOIUrl":"https://doi.org/10.1017/S0305004122000081","url":null,"abstract":"Abstract We prove uniform bounds for the Petersson norm of the cuspidal part of the theta series. This gives an improved asymptotic formula for the number of representations by a quadratic form. As an application, we show that every integer \u0000$n neq 0,4,7 ,(textrm{mod} 8)$\u0000 is represented as \u0000$n= x_1^2 + x_2^2 + x_3^3$\u0000 for integers \u0000$x_1,x_2,x_3$\u0000 such that the product \u0000$x_1x_2x_3$\u0000 has at most 72 prime divisors.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"32 1","pages":"669 - 691"},"PeriodicalIF":0.8,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80755708","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: 2
Corrigendum: towards an understanding of ramified extensions of structured ring spectra 勘误:对结构环谱的分支扩展的理解
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2020-12-02 DOI: 10.1017/S0305004120000274
B. Dundas, A. Lindenstrauss, Birgit Richter
{"title":"Corrigendum: towards an understanding of ramified extensions of structured ring spectra","authors":"B. Dundas, A. Lindenstrauss, Birgit Richter","doi":"10.1017/S0305004120000274","DOIUrl":"https://doi.org/10.1017/S0305004120000274","url":null,"abstract":"","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"418 1","pages":"247 - 248"},"PeriodicalIF":0.8,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76626941","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: 3
Fourier duality in the Brascamp–Lieb inequality Brascamp-Lieb不等式的傅里叶对偶性
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2020-11-27 DOI: 10.1017/S0305004121000608
Jonathan Bennett, Eunhee Jeong
{"title":"Fourier duality in the Brascamp–Lieb inequality","authors":"Jonathan Bennett, Eunhee Jeong","doi":"10.1017/S0305004121000608","DOIUrl":"https://doi.org/10.1017/S0305004121000608","url":null,"abstract":"Abstract It was observed recently in work of Bez, Buschenhenke, Cowling, Flock and the first author, that the euclidean Brascamp–Lieb inequality satisfies a natural and useful Fourier duality property. The purpose of this paper is to establish an appropriate discrete analogue of this. Our main result identifies the Brascamp–Lieb constants on (finitely-generated) discrete abelian groups with Brascamp–Lieb constants on their (Pontryagin) duals. As will become apparent, the natural setting for this duality principle is that of locally compact abelian groups, and this raises basic questions about Brascamp–Lieb constants formulated in this generality.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"32 1","pages":"387 - 409"},"PeriodicalIF":0.8,"publicationDate":"2020-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77667587","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: 3
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