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Erratum to “Harmonic Maass forms associated to real quadratic fields” “与实二次场相关的调和质量形式”的勘误
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-02-02 DOI: 10.4171/JEMS/1043
Pierre Charollois, Yingkun Li
{"title":"Erratum to “Harmonic Maass forms associated to real quadratic fields”","authors":"Pierre Charollois, Yingkun Li","doi":"10.4171/JEMS/1043","DOIUrl":"https://doi.org/10.4171/JEMS/1043","url":null,"abstract":"[1] Pierre Charollois, Yingkun Li, Harmonic Maass forms associated to real quadratic fields, JEMS 22, 1115–1148 (2020). [2] Yingkun Li, Markus Schwagenscheidt, Mock modular forms with integral Fourier coefficients, preprint, arxiv:2101.05583 (2021). [3] Nils Scheithauer, The Weil Representation of SL2(Z) and Some Applications, Int. Math. Res. Not., no. 8, 1488–1545 (2009). E-mail address: pierre.charollois@imj-prg.fr E-mail address: li@mathematik.tu-darmstadt.de","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"123 1","pages":"1051-1051"},"PeriodicalIF":2.6,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75686511","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
Kernels of conditional determinantal measures and the Lyons–Peres completeness conjecture
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-01-19 DOI: 10.4171/JEMS/1038
A. Bufetov, Yanqi Qiu, A. Shamov
{"title":"Kernels of conditional determinantal measures and the Lyons–Peres completeness conjecture","authors":"A. Bufetov, Yanqi Qiu, A. Shamov","doi":"10.4171/JEMS/1038","DOIUrl":"https://doi.org/10.4171/JEMS/1038","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"32 3","pages":"1477-1519"},"PeriodicalIF":2.6,"publicationDate":"2021-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72480122","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: 9
On geometrically finite degenerations I: boundaries of main hyperbolic components 几何有限退化I:主要双曲分量的边界
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-01-19 DOI: 10.4171/jems/1342
Yusheng Luo
{"title":"On geometrically finite degenerations I: boundaries of main hyperbolic components","authors":"Yusheng Luo","doi":"10.4171/jems/1342","DOIUrl":"https://doi.org/10.4171/jems/1342","url":null,"abstract":"In this paper, we develop a theory on the degenerations of Blaschke products $mathcal{B}_d$ to study the boundaries of hyperbolic components. We give a combinatorial classification of geometrically finite polynomials on the boundary of the main hyperbolic component $mathcal{H}_d$ containing $z^d$. We show the closure $overline{mathcal{H}_d}$ is not a topological manifold with boundary for $dgeq 4$ by constructing self-bumps on its boundary.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"35 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74055930","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
Hermitian operators and isometries on symmetric operator spaces 对称算子空间上的厄米算子和等距
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-01-11 DOI: 10.4171/jems/1332
Jinghao Huang, F. Sukochev
{"title":"Hermitian operators and isometries on symmetric operator spaces","authors":"Jinghao Huang, F. Sukochev","doi":"10.4171/jems/1332","DOIUrl":"https://doi.org/10.4171/jems/1332","url":null,"abstract":"Let $mathcal{M}$ be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space $H$ equipped with a semifinite faithful normal trace $tau$. Let $E(mathcal{M},tau) $ be a symmetric operator space affiliated with $ mathcal{M} $, whose norm is order continuous and is not proportional to the Hilbertian norm $left|cdotright|_2$ on $L_2(mathcal{M},tau)$. We obtain general description of all bounded hermitian operators on $E(mathcal{M},tau)$. This is the first time that the description of hermitian operators on asymmetric operator space (even for a noncommutative $L_p$-space) is obtained in the setting of general (non-hyperfinite) von Neumann algebras. As an application, we resolve a long-standing open problem concerning the description of isometries raised in the 1980s, which generalizes and unifies numerous earlier results.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"4 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87245097","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
A subspace theorem for manifolds 流形的子空间定理
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-01-11 DOI: 10.4171/jems/1346
E. Breuillard, Nicolas de Saxc'e
{"title":"A subspace theorem for manifolds","authors":"E. Breuillard, Nicolas de Saxc'e","doi":"10.4171/jems/1346","DOIUrl":"https://doi.org/10.4171/jems/1346","url":null,"abstract":"We prove a theorem that generalizes Schmidt's Subspace Theorem in the context of metric diophantine approximation. To do so we reformulate the Subspace theorem in the framework of homogeneous dynamics by introducing and studying a slope formalism and the corresponding notion of semistability for diagonal flows.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"3 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82648267","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
Lengths spectrum of hyperelliptic components 超椭圆分量的长度谱
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-01-01 DOI: 10.4171/jems/1150
Corentin Boissy, Erwan Lanneau
{"title":"Lengths spectrum of hyperelliptic components","authors":"Corentin Boissy, Erwan Lanneau","doi":"10.4171/jems/1150","DOIUrl":"https://doi.org/10.4171/jems/1150","url":null,"abstract":"We propose a general framework for studying pseudo-Anosov homeomorphisms on translation surfaces. This new approach, among other consequences, allows us to compute the systole of the Teichmüller geodesic flow restricted to the hyperelliptic connected components of the strata of Abelian differentials, settling a question of [Far06]; This is the first description of the systole in any component of any stratum outside of genus two and three. We stress that all proofs and computations can be performed without the help of a computer. As a byproduct, our methods give a way to describe the bottom of the lengths spectrum of the hyperelliptic components and we provide a picture of that for small genera.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"83 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82064803","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
Elliptic surfaces and intersections of adelic $mathbb{R}$-divisors -因子的椭圆曲面与交点
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2020-12-28 DOI: 10.4171/jems/1354
Laura Demarco, Niki Myrto Mavraki
{"title":"Elliptic surfaces and intersections of adelic $mathbb{R}$-divisors","authors":"Laura Demarco, Niki Myrto Mavraki","doi":"10.4171/jems/1354","DOIUrl":"https://doi.org/10.4171/jems/1354","url":null,"abstract":"Suppose $mathcal{E} to B$ is a non-isotrivial elliptic surface defined over a number field, for smooth projective curve $B$. Let $k$ denote the function field $overline{mathbb{Q}}(B)$ and $E$ the associated elliptic curve over $k$. In this article, we construct adelically metrized $mathbb{R}$-divisors $overline{D}_X$ on the base curve $B$ over a number field, for each $X in E(k)otimes mathbb{R}$. We prove non-degeneracy of the Arakelov-Zhang intersection numbers $overline{D}_Xcdot overline{D}_Y$, as a biquadratic form on $E(k)otimes mathbb{R}$. As a consequence, we have the following Bogomolov-type statement for the N'eron-Tate height functions on the fibers $E_t(overline{mathbb{Q}})$ of $mathcal{E}$ over $t in B(overline{mathbb{Q}})$: given points $P_1, ldots, P_m in E(k)$ with $mgeq 2$, there exist an infinite sequence $t_nin B(overline{mathbb{Q}})$ and small-height perturbations $P_{i,t_n}' in E_{t_n}(overline{mathbb{Q}})$ of specializations $P_{i,t_n}$ so that the set ${P_{1, t_n}', ldots, P_{m,t_n}'}$ satisfies at least two independent linear relations for all $n$, if and only if the points $P_1, ldots, P_m$ are linearly dependent in $E(k)$. This gives a new proof of results of Masser and Zannier and of Barroero and Capuano and extends our earlier results. In the Appendix, we prove an equidistribution theorem for adelically metrized $mathbb{R}$-divisors on projective varieties (over a number field) using results of Moriwaki, extending the equidistribution theorem of Yuan.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"35 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89210119","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
Classification and statistics of cut-and-project sets 切割和项目集的分类和统计
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2020-12-24 DOI: 10.4171/jems/1338
Ren'e Ruhr, Yotam Smilansky, B. Weiss
{"title":"Classification and statistics of cut-and-project sets","authors":"Ren'e Ruhr, Yotam Smilansky, B. Weiss","doi":"10.4171/jems/1338","DOIUrl":"https://doi.org/10.4171/jems/1338","url":null,"abstract":"We define Ratner-Marklof-Strombergsson measures. These are probability measures supported on cut-and-project sets in R^d (d>1) which are invariant and ergodic for the action of the groups ASL_d(R) or SL_d(R). We classify the measures that can arise in terms of algebraic groups and homogeneous dynamics. Using the classification, we prove analogues of results of Siegel, Weil and Rogers about a Siegel summation formula and identities and bounds involving higher moments. We deduce results about asymptotics, with error estimates, of point-counting and patch-counting for typical cut-and-project sets.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"77 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2020-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76778091","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
Level spacing and Poisson statistics for continuum random Schrödinger operators 连续统随机Schrödinger算子的水平间距和泊松统计量
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2020-12-22 DOI: 10.4171/jems/1033
Adrian Dietlein, A. Elgart
{"title":"Level spacing and Poisson statistics for continuum random Schrödinger operators","authors":"Adrian Dietlein, A. Elgart","doi":"10.4171/jems/1033","DOIUrl":"https://doi.org/10.4171/jems/1033","url":null,"abstract":"For continuum alloy-type random Schrödinger operators with signdefinite single-site bump functions and absolutely continuous single-site randomness we prove a probabilistic level-spacing estimate at the bottom of the spectrum. More precisely, given a finite-volume restriction of the random operator onto a box of linear size L, we prove that with high probability the eigenvalues below some threshold energy Esp keep a distance of at least e −(logL) for sufficiently large β > 1. This implies simplicity of the spectrum of the infinite-volume operator below Esp. Under the additional assumption of Lipschitz-continuity of the single-site probability density we also prove a Minami-type estimate and Poisson statistics for the point process given by the unfolded eigenvalues around a reference energy E.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"163 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80305832","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
General path integrals and stable SDEs 一般路径积分与稳定sde
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2020-12-14 DOI: 10.4171/jems/1331
S. Baguley, L. Doering, A. Kyprianou
{"title":"General path integrals and stable SDEs","authors":"S. Baguley, L. Doering, A. Kyprianou","doi":"10.4171/jems/1331","DOIUrl":"https://doi.org/10.4171/jems/1331","url":null,"abstract":"The theory of one-dimensional stochastic differential equations driven by Brownian motion is classical and has been largely understood for several decades. For stochastic differential equations with jumps the picture is still incomplete, and even some of the most basic questions are only partially understood. In the present article we study existence and uniqueness of weak solutions to [ \u0000{rm d}Z_t=sigma(Z_{t-}){rm d} X_t \u0000]driven by a (symmetric) $alpha$-stable Levy process, in the spirit of the classical Engelbert-Schmidt time-change approach. Extending and completing results of Zanzotto we derive a complete characterisation for existence und uniqueness of weak solutions for $alphain(0,1)$. Our approach is not based on classical stochastic calculus arguments but on the general theory of Markov processes. We proof integral tests for finiteness of path integrals under minimal assumptions.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"143 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80326543","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
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