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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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
The cube axiom and resolutions in homotopy theory 同调理论中的立方公理和决议
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-29 DOI: 10.1007/s11856-023-2582-9
Manfred Stelzer
{"title":"The cube axiom and resolutions in homotopy theory","authors":"Manfred Stelzer","doi":"10.1007/s11856-023-2582-9","DOIUrl":"https://doi.org/10.1007/s11856-023-2582-9","url":null,"abstract":"<p>We show that a version of the cube axiom holds in cosimplicial unstable coalgebras and cosimplicial spaces equipped with a resolution model structure. As an application, classical theorems in unstable homotopy theory are extended to this context.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579571","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
Homology of the pronilpotent completion and cotorsion groups 代势完成群和反转群的同源性
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-29 DOI: 10.1007/s11856-023-2579-4
Mikhail Basok, Sergei O. Ivanov, Roman Mikhailov
{"title":"Homology of the pronilpotent completion and cotorsion groups","authors":"Mikhail Basok, Sergei O. Ivanov, Roman Mikhailov","doi":"10.1007/s11856-023-2579-4","DOIUrl":"https://doi.org/10.1007/s11856-023-2579-4","url":null,"abstract":"<p>For a non-cyclic free group <i>F</i>, the second homology of its pronilpotent completion <span>({H_2}(widehat F))</span> is not a cotorsion group.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579743","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
Notes on restriction theory in the primes 关于质点限制理论的说明
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-29 DOI: 10.1007/s11856-023-2586-5
Olivier Ramaré
{"title":"Notes on restriction theory in the primes","authors":"Olivier Ramaré","doi":"10.1007/s11856-023-2586-5","DOIUrl":"https://doi.org/10.1007/s11856-023-2586-5","url":null,"abstract":"<p>We study the mean <span>(sumnolimits_{x in {cal X}} {|sumnolimits_{p le N} {{u_p}e(xp){|^ell}}} )</span> when ℓ covers the full range [2, ∞) and <span>({cal X} subset mathbb{R}/mathbb{Z})</span> is a well-spaced set, providing a smooth transition from the case ℓ = 2 to the case ℓ &gt; 2 and improving on the results of J. Bourgain and of B. Green and T. Tao. A uniform Hardy–Littlewood property for the set of primes is established as well as a sharp upper bound for <span>(sumnolimits_{x in {cal X}} {|sumnolimits_{p le N} {{u_p}e(xp){|^ell}}})</span> when <span>({cal X})</span> is small. These results are extended to primes in any interval in a last section, provided the primes are numerous enough therein.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579624","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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