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On the largest prime factor of $n^2+1$ n^2+1的最大质因数
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-02-04 DOI: 10.4171/jems/1216
Jori Merikoski
{"title":"On the largest prime factor of $n^2+1$","authors":"Jori Merikoski","doi":"10.4171/jems/1216","DOIUrl":"https://doi.org/10.4171/jems/1216","url":null,"abstract":"We show that the largest prime factor of $n^2+1$ is infinitely often greater than $n^{1.279}$. This improves the result of de la Bret`eche and Drappeau (2019) who obtained this with $1.2182$ in place of $1.279.$ The main new ingredients in the proof are a new Type II estimate and using this estimate by applying Harman's sieve method. To prove the Type II estimate we use the bounds of Dehouillers and Iwaniec on linear forms of Kloosterman sums. We also show that conditionally on Selberg's eigenvalue conjecture the exponent $1.279$ may be increased to $1.312.$","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"5 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503874","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
An ultimate proof of Hoffmann–Totaro’s conjecture Hoffmann-Totaro猜想的终极证明
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-01-28 DOI: 10.4171/jems/1211
N. Karpenko
{"title":"An ultimate proof of Hoffmann–Totaro’s conjecture","authors":"N. Karpenko","doi":"10.4171/jems/1211","DOIUrl":"https://doi.org/10.4171/jems/1211","url":null,"abstract":"We prove the last open case of the conjecture on the possible values of the first isotropy index of an anisotropic quadratic form over a field. It was initially stated by Detlev Hoffmann for fields of characteristic ̸= 2 and then extended to arbitrary characteristic by Burt Totaro. The initial statement was proven by the author in 2002. In characteristic 2, the case of a totally singular quadratic form was done by Stephen Scully in 2015 and the nonsingular case by Eric Primozic in early 2019.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"384 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74741293","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
Erratum to “Uniform K-stability and asymptotics of energy functionals in Kähler geometry” “Kähler几何中能量泛函的一致k -稳定性和渐近性”的勘误
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2022-01-13 DOI: 10.4171/jems/1215
S. Boucksom, Tomoyuki Hisamoto, Mattias Jonsson
{"title":"Erratum to “Uniform K-stability and asymptotics of energy functionals in Kähler geometry”","authors":"S. Boucksom, Tomoyuki Hisamoto, Mattias Jonsson","doi":"10.4171/jems/1215","DOIUrl":"https://doi.org/10.4171/jems/1215","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"40 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81451536","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
Local convergence of random planar graphs 随机平面图的局部收敛性
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-11-17 DOI: 10.4171/jems/1174
Benedikt Stufler
{"title":"Local convergence of random planar graphs","authors":"Benedikt Stufler","doi":"10.4171/jems/1174","DOIUrl":"https://doi.org/10.4171/jems/1174","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"10 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503873","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
Irreducible modules for pseudo-reductive groups 伪约化群的不可约模
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-11-09 DOI: 10.4171/jems/1153
Michael Bate, David I. Stewart
{"title":"Irreducible modules for pseudo-reductive groups","authors":"Michael Bate, David I. Stewart","doi":"10.4171/jems/1153","DOIUrl":"https://doi.org/10.4171/jems/1153","url":null,"abstract":"We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive groups to the split reductive case and the pseudo-split pseudo-reductive commutative case. Moreover, we give the first results on the latter, including a rather complete description of the rank one case.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"11 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503872","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
$mathbb{C}$-motivic modular forms $mathbb{C}$-动机模块形式
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-11-09 DOI: 10.4171/jems/1171
Bogdan Gheorghe, Daniel Isaksen, Achim Krause, N. Ricka
{"title":"$mathbb{C}$-motivic modular forms","authors":"Bogdan Gheorghe, Daniel Isaksen, Achim Krause, N. Ricka","doi":"10.4171/jems/1171","DOIUrl":"https://doi.org/10.4171/jems/1171","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"19 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85334215","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
Landau–Ginzburg mirror symmetry conjecture 朗道-金兹堡镜像对称猜想
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-11-05 DOI: 10.4171/jems/1155
Weiqiang He, Si Li, Yefeng Shen, Rachel Webb
{"title":"Landau–Ginzburg mirror symmetry conjecture","authors":"Weiqiang He, Si Li, Yefeng Shen, Rachel Webb","doi":"10.4171/jems/1155","DOIUrl":"https://doi.org/10.4171/jems/1155","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"5 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79568127","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
Summability of the coefficients of a multilinear form 多线性形式的系数的可和性
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-07-21 DOI: 10.4171/JEMS/1109
F. Bayart
{"title":"Summability of the coefficients of a multilinear form","authors":"F. Bayart","doi":"10.4171/JEMS/1109","DOIUrl":"https://doi.org/10.4171/JEMS/1109","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"8 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72713098","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: 6
On the distribution of ${Cl}(K)[l^infty]$ for degree $l$ cyclic fields 关于次$l$循环场${Cl}(K)[l^infty]$的分布
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-07-20 DOI: 10.4171/JEMS/1112
P. Koymans, Carlo Pagano
{"title":"On the distribution of ${Cl}(K)[l^infty]$ for degree $l$ cyclic fields","authors":"P. Koymans, Carlo Pagano","doi":"10.4171/JEMS/1112","DOIUrl":"https://doi.org/10.4171/JEMS/1112","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"12 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85013265","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
On a class number formula of Hurwitz 关于Hurwitz的一个类数公式
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-05-25 DOI: 10.4171/JEMS/1097
W. Duke, Ö. Imamoḡlu, Á. Tóth
{"title":"On a class number formula of Hurwitz","authors":"W. Duke, Ö. Imamoḡlu, Á. Tóth","doi":"10.4171/JEMS/1097","DOIUrl":"https://doi.org/10.4171/JEMS/1097","url":null,"abstract":"In a little-known paper Hurwitz gave an infinite series representation of the class number for positive definite binary quadratic forms. In this paper we give a similar formula in the indefinite case. We also give a simple proof of Hurwitz’s formula and indicate some extensions.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"29 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75556520","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
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