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Disproving Hooley’s conjecture 反驳胡利的猜想
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-11-03 DOI: 10.4171/jems/1291
D. Fiorilli, G. Martin
{"title":"Disproving Hooley’s conjecture","authors":"D. Fiorilli, G. Martin","doi":"10.4171/jems/1291","DOIUrl":"https://doi.org/10.4171/jems/1291","url":null,"abstract":". Define G ( x ; q ) to be the variance of primes p ≤ x in the arithmetic progressions modulo q , weighted by log p . In analogy with his q -analogue of Selberg’s upper bound on the variance of primes in intervals, Hooley conjectured that as soon as q tends to infinity and x ≥ q , we have the upper bound G ( x ; q ) (cid:28) x log q . This conjecture was proven true over function fields by Keating and Rudnick, using equidistribution results of Katz. In this paper we show that the upper bound does not hold in general, and that G ( x ; q ) can be much larger than x log q for values of q which are (cid:16) log log x . This implies that a conjecture of the first author on the range of validity of Hooley’s conjecture is essentially best possible.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84086039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Erdős–Szekeres theorem for multidimensional arrays Erdős-Szekeres多维数组定理
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-08-31 DOI: 10.4171/jems/1262
Matija Bucić, B. Sudakov, T. Tran
{"title":"Erdős–Szekeres theorem for multidimensional arrays","authors":"Matija Bucić, B. Sudakov, T. Tran","doi":"10.4171/jems/1262","DOIUrl":"https://doi.org/10.4171/jems/1262","url":null,"abstract":"The classical Erdős-Szekeres theorem dating back almost a hundred years states that any sequence of (n − 1) + 1 distinct real numbers contains a monotone subsequence of length n. This theorem has been generalised to higher dimensions in a variety of ways but perhaps the most natural one was proposed by Fishburn and Graham more than 25 years ago. They defined the concept of a monotone and a lex-monotone array and asked how large an array one needs in order to be able to find a monotone or a lex-monotone subarray of size n× . . .×n. Fishburn and Graham obtained Ackerman-type bounds in both cases. We significantly improve these results. Regardless of the dimension we obtain at most a triple exponential bound in n in the monotone case and a quadruple exponential one in the lex-monotone case.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88030072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 12
Multiplicity one theorems for the generalized doubling method (with an appendix by Avraham Aizenbud and Dmitry Gourevitch) 广义加倍法的多重性定理(附Avraham Aizenbud和Dmitry Gourevitch的附录)
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-07-28 DOI: 10.4171/jems/1207
D. Gourevitch, Eyal Kaplan
{"title":"Multiplicity one theorems for the generalized doubling method (with an appendix by Avraham Aizenbud and Dmitry Gourevitch)","authors":"D. Gourevitch, Eyal Kaplan","doi":"10.4171/jems/1207","DOIUrl":"https://doi.org/10.4171/jems/1207","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74020506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 singularity formation for the two-dimensional unsteady Prandtl system around the axis 绕轴二维非定常普朗特系统奇点的形成
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-07-12 DOI: 10.4171/jems/1240
Charles Collot, T. Ghoul, S. Ibrahim, N. Masmoudi
{"title":"On singularity formation for the two-dimensional unsteady Prandtl system around the axis","authors":"Charles Collot, T. Ghoul, S. Ibrahim, N. Masmoudi","doi":"10.4171/jems/1240","DOIUrl":"https://doi.org/10.4171/jems/1240","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78660894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
The classification of dp-minimal and dp-small fields dp极小域和dp小域的分类
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-07-08 DOI: 10.4171/jems/1187
Will Johnson
{"title":"The classification of dp-minimal and dp-small fields","authors":"Will Johnson","doi":"10.4171/jems/1187","DOIUrl":"https://doi.org/10.4171/jems/1187","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86471604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Rationality and fusion rules of exceptional $mathcal {W}$-algebras 例外$mathcal {W}$-代数的合理性及融合规则
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-06-24 DOI: 10.4171/jems/1250
T. Arakawa, Jethro van Ekeren
{"title":"Rationality and fusion rules of exceptional $mathcal {W}$-algebras","authors":"T. Arakawa, Jethro van Ekeren","doi":"10.4171/jems/1250","DOIUrl":"https://doi.org/10.4171/jems/1250","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90177963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Proper base change for étale sheaves of spaces 适当的基础变化，以适应空间的变化
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-06-24 DOI: 10.4171/jems/1263
Chang-Yeon Chough
{"title":"Proper base change for étale sheaves of spaces","authors":"Chang-Yeon Chough","doi":"10.4171/jems/1263","DOIUrl":"https://doi.org/10.4171/jems/1263","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85511457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 4
Erratum to “Uniform boundary controllability and homogenization of wave equations” “波动方程的均匀边界可控性和均匀化”的勘误
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-05-12 DOI: 10.4171/jems/1261
F. Lin, Zhongwei Shen
{"title":"Erratum to “Uniform boundary controllability and homogenization of wave equations”","authors":"F. Lin, Zhongwei Shen","doi":"10.4171/jems/1261","DOIUrl":"https://doi.org/10.4171/jems/1261","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80950175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Effective joint equidistribution of primitive rational points on expanding horospheres 扩展天球上原始有理点的有效联合均分
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-04-26 DOI: 10.4171/jems/1238
Daniel El-Baz,Bingrong Huang,Min Lee
{"title":"Effective joint equidistribution of primitive rational points on expanding horospheres","authors":"Daniel El-Baz,Bingrong Huang,Min Lee","doi":"10.4171/jems/1238","DOIUrl":"https://doi.org/10.4171/jems/1238","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Commensurated subgroups and micro-supported actions (with an appendix by Dominik Francoeur) 通约子群和微支持行动(附多米尼克·弗朗索瓦的附录)
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-04-13 DOI: 10.4171/jems/1236
P. Caprace, Adrien Le Boudec
{"title":"Commensurated subgroups and micro-supported actions (with an appendix by Dominik Francoeur)","authors":"P. Caprace, Adrien Le Boudec","doi":"10.4171/jems/1236","DOIUrl":"https://doi.org/10.4171/jems/1236","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79249149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
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