Mathematische Annalen最新文献_第8页

Finding large additive and multiplicative Sidon sets in sets of integers 在整数集合中寻找大的加法和乘法西顿集合

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-07-08 DOI: 10.1007/s00208-024-02932-7

Yifan Jing, Akshat Mudgal

{"title":"Finding large additive and multiplicative Sidon sets in sets of integers","authors":"Yifan Jing, Akshat Mudgal","doi":"10.1007/s00208-024-02932-7","DOIUrl":"https://doi.org/10.1007/s00208-024-02932-7","url":null,"abstract":"Given (h,g in {mathbb {N}}), we write a set (X subset {mathbb {Z}}) to be a (B_{h}^{+}[g]) set if for any (n in {mathbb {Z}}), the number of solutions to the additive equation (n = x_1 + dots + x_h) with (x_1, dots , x_h in X) is at most g, where we consider two such solutions to be the same if they differ only in the ordering of the summands. We define a multiplicative (B_{h}^{times }[g]) set analogously. In this paper, we prove, amongst other results, that there exist absolute constants (g in {mathbb {N}}) and (delta >0) such that for any (h in {mathbb {N}}) and for any finite set A of integers, the largest (B_{h}^{+}[g]) set B inside A and the largest (B_{h}^{times }[g]) set C inside A satisfy $$begin{aligned} max { |B|, |C| } gg _{h} |A|^{(1+ delta )/h }. end{aligned}$$In fact, when (h=2), we may set (g = 31), and when h is sufficiently large, we may set (g = 1) and (delta gg (log log h)^{1/2 - o(1)}). The former makes progress towards a recent conjecture of Klurman–Pohoata and quantitatively strengthens previous work of Shkredov.","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"16 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Sections of convex bodies and Hanner polytopes 凸体的截面和汉纳多面体

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-07-05 DOI: 10.1007/s00208-024-02930-9

Xinbao Lu, Jiangyan Tao, Ge Xiong

引用次数: 0

A note on the paper 文件说明

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-07-02 DOI: 10.1007/s00208-024-02926-5

Nesrine Aroua, Mourad Bellassoued

引用次数: 0

Globally solvable time-periodic evolution equations in Gelfand–Shilov classes 格尔方-希洛夫类中全局可解的时周期演化方程

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-07-01 DOI: 10.1007/s00208-024-02925-6

Fernando de Ávila Silva, Marco Cappiello

引用次数: 0

Factoring non-negative operator valued trigonometric polynomials in two variables 因式分解两变量中的非负算子值三角多项式

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-06-27 DOI: 10.1007/s00208-024-02895-9

Michael A. Dritschel

引用次数: 0

Diagonals of self-adjoint operators II: non-compact operators 自相加算子的对角线 II：非紧凑算子

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-06-23 DOI: 10.1007/s00208-024-02910-z

Marcin Bownik, John Jasper

{"title":"Diagonals of self-adjoint operators II: non-compact operators","authors":"Marcin Bownik, John Jasper","doi":"10.1007/s00208-024-02910-z","DOIUrl":"https://doi.org/10.1007/s00208-024-02910-z","url":null,"abstract":"Given a self-adjoint operator T on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set ({mathcal {D}}(T)) of all possible diagonals of T. For operators T with at least two points in their essential spectrum (sigma _{ess}(T)), we give a complete characterization of ({mathcal {D}}(T)) for the class of self-adjoint operators sharing the same spectral measure as T with a possible exception of multiplicities of eigenvalues at the extreme points of (sigma _{ess}(T)). We also give a more precise description of ({mathcal {D}}(T)) for a fixed self-adjoint operator T, albeit modulo the kernel problem for special classes of operators. These classes consist of operators T for which an extreme point of the essential spectrum (sigma _{ess}(T)) is also an extreme point of the spectrum (sigma (T)). Our results generalize a characterization of diagonals of orthogonal projections by Kadison [38, 39], Blaschke-type results of Müller and Tomilov [51] and Loreaux and Weiss [48], and a characterization of diagonals of operators with finite spectrum by the authors [15].","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"36 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Spectral moment formulae for $$GL(3)times GL(2)$$ L-functions III: the twisted case $$GL(3)/times GL(2)$$ L 函数的谱矩公式 III：扭曲情况

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-06-21 DOI: 10.1007/s00208-024-02914-9

Chung-Hang Kwan

引用次数: 0

Recognition of Seifert fibered spaces with boundary is in NP 有边界的塞弗特纤维空间的识别在 NP 中

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-06-20 DOI: 10.1007/s00208-024-02920-x

Adele Jackson

引用次数: 0

Global existence of entropy solutions for euler equations of compressible fluid flow 可压缩流体流动欧拉方程熵解的全局存在性