{"title":"Monotonicity and phase transition for the VRJP and the ERRW","authors":"Rémy Poudevigne-Auboiron","doi":"10.4171/jems/1298","DOIUrl":"https://doi.org/10.4171/jems/1298","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"58 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72550769","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}
{"title":"Subconvexity for $L$-functions on $operatorname{GL}_3$ over number fields","authors":"Zhi Qi","doi":"10.4171/jems/1306","DOIUrl":"https://doi.org/10.4171/jems/1306","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"107 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76831962","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}
{"title":"Between reduced powers and ultrapowers","authors":"I. Farah","doi":"10.4171/jems/1279","DOIUrl":"https://doi.org/10.4171/jems/1279","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"7 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78462819","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}
{"title":"A simple $P_{aleph_1}$-point and a simple $P_{aleph_2}$-point","authors":"Christian Bräuninger, H. Mildenberger","doi":"10.4171/jems/1299","DOIUrl":"https://doi.org/10.4171/jems/1299","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"110 2 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83889129","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}
{"title":"Dynamics of a periodic-parabolic Lotka–Volterra competition-diffusion system in heterogeneous environments","authors":"Xueli Bai, Xiaoqing He, W. Ni","doi":"10.4171/jems/1296","DOIUrl":"https://doi.org/10.4171/jems/1296","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"23 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87627453","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}
. 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.
{"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":"49 1","pages":""},"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}
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.
{"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":"311 1","pages":""},"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}
{"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":"23 1","pages":""},"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}
{"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":"2008 1","pages":""},"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}
{"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":"1 1","pages":""},"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}
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