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Probabilistic hypergraph containers 概率超图容器
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-12-18 DOI: 10.1007/s11856-023-2602-9
Rajko Nenadov
{"title":"Probabilistic hypergraph containers","authors":"Rajko Nenadov","doi":"10.1007/s11856-023-2602-9","DOIUrl":"https://doi.org/10.1007/s11856-023-2602-9","url":null,"abstract":"<p>Given a <i>k</i>-uniform hypergraph ℋ and sufficiently large <i>m</i> ≫ <i>m</i><sub>0</sub>(ℋ), we show that an m-element set <i>I</i> ⊆ <i>V</i>(ℋ), chosen uniformly at random, with probability 1 − <i>e−</i><sup><i>ω</i>(<i>m</i>)</sup> is either not independent or is contained in an almost-independent set in ℋ which, crucially, can be constructed from carefully chosen <i>o</i>(<i>m</i>) vertices of <i>I</i>. As a corollary, this implies that if the largest almost-independent set in ℋ is of size <i>o</i>(<i>v</i>(ℋ)) then <i>I</i> itself is an independent set with probability <i>e</i><sup><i>−ω</i>(<i>m</i>)</sup>. More generally, <i>I</i> is very likely to inherit structural properties of almost-independent sets in ℋ.</p><p>The value <i>m</i><sub>0</sub>(ℋ) coincides with that for which Janson’s inequality gives that <i>I</i> is independent with probability at most <span>({e^{- Theta ({m_0})}})</span>. On the one hand, our result is a significant strengthening of Janson’s inequality in the range <i>m</i> ≫ <i>m</i><sub>0</sub>. On the other hand, it can be seen as a probabilistic variant of hypergraph container theorems, developed by Balogh, Morris and Samotij and, independently, by Saxton and Thomason. While being strictly weaker than the original container theorems in the sense that it does not apply to all independent sets of size <i>m</i>, it is nonetheless sufficient for many applications and admits a short proof using probabilistic ideas.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"29 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030703","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
Bernoullicity of lopsided principal algebraic actions 片面主代数作用的伯努利性
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-12-18 DOI: 10.1007/s11856-023-2594-5
Hanfeng Li, Kairan Liu
{"title":"Bernoullicity of lopsided principal algebraic actions","authors":"Hanfeng Li, Kairan Liu","doi":"10.1007/s11856-023-2594-5","DOIUrl":"https://doi.org/10.1007/s11856-023-2594-5","url":null,"abstract":"<p>We show that the principal algebraic actions of countably infinite groups associated to lopsided elements in the integral group ring satisfying some orderability condition are Bernoulli.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"88 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030889","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
Effective Hilbert’s irreducibility theorem for global fields 全域的有效希尔伯特不可还原性定理
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-12-18 DOI: 10.1007/s11856-023-2604-7
Marcelo Paredes, Román Sasyk
{"title":"Effective Hilbert’s irreducibility theorem for global fields","authors":"Marcelo Paredes, Román Sasyk","doi":"10.1007/s11856-023-2604-7","DOIUrl":"https://doi.org/10.1007/s11856-023-2604-7","url":null,"abstract":"<p>We prove an effective form of Hilbert’s irreducibility theorem for polynomials over a global field <i>K</i>. More precisely, we give effective bounds for the number of specializations <span>(t in {{cal O}_K})</span> that do not preserve the irreducibility or the Galois group of a given irreducible polynomial <i>F</i>(<i>T, Y</i>) ∈ <i>K</i>[<i>T, Y</i>]. The bounds are explicit in the height and degree of the polynomial <i>F</i>(<i>T, Y</i>), and are optimal in terms of the size of the parameter <span>(t in {{cal O}_K})</span>. Our proofs deal with the function field and number field cases in a unified way.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"15 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030600","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
Locally harmonic Maass forms of positive even weight 正偶数重的局部谐波马斯形式
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-12-18 DOI: 10.1007/s11856-023-2592-7
Andreas Mono
{"title":"Locally harmonic Maass forms of positive even weight","authors":"Andreas Mono","doi":"10.1007/s11856-023-2592-7","DOIUrl":"https://doi.org/10.1007/s11856-023-2592-7","url":null,"abstract":"<p>We twist Zagier’s function <i>f</i><sub><i>k,D</i></sub> by a sign function and a genus character. Assuming weight 0 &lt; <i>k</i> ≡ 2 (mod 4), and letting <i>D</i> be a positive non-square discriminant, we prove that the obstruction to modularity caused by the sign function can be corrected obtaining a locally harmonic Maaß form or a local cusp form of the same weight. In addition, we provide an alternative representation of our new function in terms of a twisted trace of modular cycle integrals of a Poincaré series due to Petersson.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"9 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030607","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
Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map 对双曲流遍历理论的贡献：准不变度量的唯一遍历性和时间一映射的均衡状态
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-12-18 DOI: 10.1007/s11856-023-2588-3
Pablo D. Carrasco, Federico Rodriguez-Hertz
{"title":"Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map","authors":"Pablo D. Carrasco, Federico Rodriguez-Hertz","doi":"10.1007/s11856-023-2588-3","DOIUrl":"https://doi.org/10.1007/s11856-023-2588-3","url":null,"abstract":"<p>We consider the horocyclic flow corresponding to a (topologically mixing) Anosov flow or diffeomorphism, and establish the uniqueness of transverse quasi-invariant measures with Hölder Jacobians. In the same setting, we give a precise characterization of the equilibrium states of the hyperbolic system, showing that existence of a family of Radon measures on the horocyclic foliation such that any probability (invariant or not) having conditionals given by this family, necessarily is the unique equilibrium state of the system.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"15 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030570","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
Waring–Goldbach problem in short intervals 短间隔中的瓦林-戈尔巴赫问题
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-12-18 DOI: 10.1007/s11856-023-2590-9
Mengdi Wang
{"title":"Waring–Goldbach problem in short intervals","authors":"Mengdi Wang","doi":"10.1007/s11856-023-2590-9","DOIUrl":"https://doi.org/10.1007/s11856-023-2590-9","url":null,"abstract":"<p>Let <i>k</i> ≥ 2 and <i>s</i> be positive integers. Let <i>θ</i> ∈ (0, 1) be a real number. In this paper, we establish that if <i>s</i> &gt; <i>k</i>(<i>k</i> + 1) and <i>θ</i> &gt; 0.55, then every sufficiently large natural number <i>n</i>, subject to certain congruence conditions, can be written as </p><span>$$n = p_1^k + cdots + p_s^k,$$</span><p>, where <i>p</i><sub><i>i</i></sub> (1 ≤ <i>i</i> ≤ <i>s</i>) are primes in the interval <span>(({({n over s})^{{1 over k}}} - {n^{{theta over k}}},{({n over s})^{{1 over k}}} + {n^{{theta over k}}}])</span>. The second result of this paper is to show that if <span>(s &gt; {{k(k + 1)} over 2})</span> and <i>θ</i> &gt; 0.55, then almost all integers <i>n</i>, subject to certain congruence conditions, have the above representation.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"46 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030601","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
Short homology bases for hyperelliptic hyperbolic surfaces 超椭圆双曲面的短同调基
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-12-18 DOI: 10.1007/s11856-023-2600-y
Peter Buser, Eran Makover, Bjoern Muetzel
{"title":"Short homology bases for hyperelliptic hyperbolic surfaces","authors":"Peter Buser, Eran Makover, Bjoern Muetzel","doi":"10.1007/s11856-023-2600-y","DOIUrl":"https://doi.org/10.1007/s11856-023-2600-y","url":null,"abstract":"<p>Given a hyperelliptic hyperbolic surface <i>S</i> of genus <i>g</i> ≥ 2, we find bounds on the lengths of homologically independent loops on <i>S</i>. As a consequence, we show that for any λ ∈ (0, 1) there exists a constant <i>N</i>(λ) such that every such surface has at least <span>(leftlceil {lambda cdot {2 over 3}g} rightrceil )</span> homologically independent loops of length at most <i>N</i>(λ), extending the result in [Mu] and [BPS]. This allows us to extend the constant upper bound obtained in [Mu] on the minimal length of non-zero period lattice vectors of hyperelliptic Riemann surfaces to almost <span>({2 over 3}g)</span> linearly independent vectors.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"243 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030598","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
On parabolic subgroups of Artin groups 论阿尔丁群的抛物面子群
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-12-18 DOI: 10.1007/s11856-023-2597-2
Philip Möller, Luis Paris, Olga Varghese
{"title":"On parabolic subgroups of Artin groups","authors":"Philip Möller, Luis Paris, Olga Varghese","doi":"10.1007/s11856-023-2597-2","DOIUrl":"https://doi.org/10.1007/s11856-023-2597-2","url":null,"abstract":"<p>Given an Artin group <i>A</i><sub>Γ</sub>, a common strategy in the study of <i>A</i><sub>Γ</sub> is the reduction to parabolic subgroups whose defining graphs have small diameter, i.e., showing that <i>A</i><sub>Γ</sub> has a specific property if and only if all “small” parabolic subgroups of <i>A</i><sub>Γ</sub> have this property. Since “small” parabolic subgroups are the building blocks of <i>A</i><sub>Γ</sub> one needs to study their behavior, in particular their intersections. The conjecture we address here says that the class of parabolic subgroups of <i>A</i><sub>Γ</sub> is closed under intersection. Under the assumption that intersections of parabolic subgroups in complete Artin groups are parabolic, we show that the intersection of a complete parabolic subgroup with an arbitrary parabolic subgroup is parabolic. Further, we connect the intersection behavior of complete parabolic subgroups of <i>A</i><sub>Γ</sub> to fixed point properties and to automatic continuity of <i>A</i><sub>Γ</sub> using Bass–Serre theory and a generalization of the Deligne complex.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"35 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030603","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
Hall’s universal group is a subgroup of the abstract commensurator of a free group 霍尔普遍群是自由群的抽象换元子群
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-12-18 DOI: 10.1007/s11856-023-2591-8
Edgar A. Bering, Daniel Studenmund
{"title":"Hall’s universal group is a subgroup of the abstract commensurator of a free group","authors":"Edgar A. Bering, Daniel Studenmund","doi":"10.1007/s11856-023-2591-8","DOIUrl":"https://doi.org/10.1007/s11856-023-2591-8","url":null,"abstract":"<p>P. Hall constructed a universal countable locally finite group <i>U</i>, determined up to isomorphism by two properties: every finite group <i>C</i> is a subgroup of <i>U</i>, and every embedding of <i>C</i> into <i>U</i> is conjugate in <i>U</i>. Every countable locally finite group is a subgroup of <i>U</i>. We prove that <i>U</i> is a subgroup of the abstract commensurator of a finite-rank nonabelian free group.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"46 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030631","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
The newform K-type and p-adic spherical harmonics 新形式 K 型和 p-二次球面谐波
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-29 DOI: 10.1007/s11856-023-2581-x
Peter Humphries
{"title":"The newform K-type and p-adic spherical harmonics","authors":"Peter Humphries","doi":"10.1007/s11856-023-2581-x","DOIUrl":"https://doi.org/10.1007/s11856-023-2581-x","url":null,"abstract":"<p>Let <span>(K: = {rm{G}}{{rm{L}}_n}({cal O}))</span> denote the maximal compact subgroup of GL<sub><i>n</i></sub>(<i>F</i>), where <i>F</i> is a nonarchimedean local field with ring of integers <span>({cal O})</span>. We study the decomposition of the space of locally constant functions on the unit sphere in <i>F</i><sup><i>n</i></sup> into irreducible <i>K</i>-modules; for <i>F</i> = ℚ<sub><i>p</i></sub>, these are the <i>p</i>-adic analogues of spherical harmonics. As an application, we characterise the newform and conductor exponent of a generic irreducible admissible smooth representation of GL<sub><i>n</i></sub>(<i>F</i>) in terms of distinguished <i>K</i>-types. Finally, we compare our results to analogous results in the archimedean setting.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"3 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579508","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
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