Let 𝔤=𝔤0¯⊕𝔤1¯{{mathfrak{g}}={mathfrak{g}}_{bar{0}}oplus{mathfrak{g}}_{bar{1}}} be a basic classical Lie superalgebra over an algebraically closed field 𝐤{{mathbf{k}}} of characteristic p>2{p>2}. Denote by 𝒵{mathcal{Z}} the center of the universal enveloping algebra U(𝔤){U({mathfrak{g}})}. Then 𝒵{mathcal{Z}} turns out to be finitely-generated purely-even commutative algebra without nonzero divisors. In this paper, we demonstrate that the fraction Frac
In this paper, we study representations of non-finitely graded Lie algebras 𝒲(ϵ){mathcal{W}(epsilon)} related to Virasoro algebra, where ϵ=±1{epsilon=pm 1}. Precisely speaking, we completely classify the free 𝒰(𝔥){mathcal{U}(mathfrak{h})}-modules of rank one over 𝒲(ϵ){mathcal{W}(epsilon)}, and find that these module structures are rather different from those of other graded Lie algebras. We also determine the simplicity and isomorphism classes of these modules.
We start a systematic analysis of the first-order model theory of free lattices. Firstly, we prove that the free lattices of finite rank are not positively indistinguishable, as there is a positive ∃∀{existsforall}-sentence true in 𝐅3{mathbf{F}_{3}} and false in 𝐅4{mathbf{F}_{4}}. Secondly, we show that every model of Th(𝐅n)
首先，我们证明有限秩的自由网格不是正向不可分的，因为在𝐅 3 {mathbf{F}_{3}} 中有一个正∃ ∀ {existsforall} -句为真，在𝐅 4 {mathbf{F}_{4}} 中为假。 .其次，我们证明了 Th ( 𝐅 n ) 的每一个模型 {mathrm{Th}(mathbf{F}_{n})}的每个模型都有一个同构的规范，可以同构到𝐇 n {mathbf{H}_{n}} 的廓界完备𝐅 n {mathbf{F}_{n} 中。｝ .第三，我们证明𝐇 n {mathbf{H}_{n}} 与𝐅 n {mathbf{F}_{n}} 的 Dedekind-MacNeille 完成同构。 并且𝐇 n {mathbf{H}_{n}} 并不等价于 𝐅 n {mathbf{F}_{n}} 的正元素。 因为有一个正 ∀ ∃ {forallexists} - 句子在𝐇 n {mathbf{{H}_{n}} 中为真，在𝐅 n {mathbf{F}_{n}} 中为假。 .最后，我们证明 DM
{"title":"Elementary properties of free lattices","authors":"J. B. Nation, Gianluca Paolini","doi":"10.1515/forum-2023-0358","DOIUrl":"https://doi.org/10.1515/forum-2023-0358","url":null,"abstract":"\u0000 <jats:p>We start a systematic analysis of the first-order model theory of free lattices.\u0000Firstly, we prove that the free lattices of finite rank are not positively indistinguishable, as there is a positive <jats:inline-formula id=\"j_forum-2023-0358_ineq_9999\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mo>∃</m:mo>\u0000 <m:mo>∀</m:mo>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0358_eq_0193.png\"/>\u0000 <jats:tex-math>{existsforall}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>-sentence true in <jats:inline-formula id=\"j_forum-2023-0358_ineq_9998\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:msub>\u0000 <m:mi>𝐅</m:mi>\u0000 <m:mn>3</m:mn>\u0000 </m:msub>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0358_eq_0215.png\"/>\u0000 <jats:tex-math>{mathbf{F}_{3}}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula> and false in <jats:inline-formula id=\"j_forum-2023-0358_ineq_9997\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:msub>\u0000 <m:mi>𝐅</m:mi>\u0000 <m:mn>4</m:mn>\u0000 </m:msub>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0358_eq_0216.png\"/>\u0000 <jats:tex-math>{mathbf{F}_{4}}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>. Secondly, we show that every model of <jats:inline-formula id=\"j_forum-2023-0358_ineq_9996\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mi>Th</m:mi>\u0000 <m:mo></m:mo>\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:msub>\u0000 <m:mi>𝐅</m:mi>\u0000 <m:mi>n</m:mi>\u0000 </m:msub>\u0000 <m:mo stretchy=\"false\">)</m:mo>\u0000 </m:mrow>\u0000 ","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140977265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, Guo and Tang independently established some q-supercongruences from Rahman’s quadratic transformation. In this paper, by applying the method of creative microscoping devised by Guo and Zudilin together with Rahman’s quadratic transformation again, we provide proofs for eight conjectures on q-supercongruences proposed by Guo and by Tang.
{"title":"Proof of some conjectures of Guo and of Tang","authors":"Guoping Gu, Xiaoxia Wang","doi":"10.1515/forum-2024-0101","DOIUrl":"https://doi.org/10.1515/forum-2024-0101","url":null,"abstract":"\u0000 Recently, Guo and Tang independently established some q-supercongruences from Rahman’s quadratic transformation.\u0000In this paper, by applying the method of creative microscoping devised by Guo and Zudilin together with Rahman’s quadratic transformation again,\u0000we provide proofs for eight conjectures on q-supercongruences proposed by Guo and by Tang.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Absolute Subspace Theorem, a vast generalization and a quantitative improvement of Schmidt’s Subspace Theorem, was first established by Evertse and Schlickewei and then strengthened remarkably by Evertse and Ferretti. We study quantitative generalizations and extensions of subspace theorems in various contexts. We establish a generalization of Evertse and Ferretti’s Absolute Subspace Theorem for hyperplanes in general position. We obtain improved (non-absolute) Quantitative Subspace Theorems for hyperplanes in general position and in subgeneral position. We show a Semi-quantitative Subspace Theorem for hyperplanes in non-subdegenerate position.
{"title":"On Absolute and Quantitative Subspace Theorems","authors":"Hieu-Truong Ngo, S. Quang","doi":"10.1515/forum-2023-0247","DOIUrl":"https://doi.org/10.1515/forum-2023-0247","url":null,"abstract":"\u0000 The Absolute Subspace Theorem, a vast generalization and a quantitative improvement of Schmidt’s Subspace Theorem, was first established by Evertse and Schlickewei and then strengthened remarkably by Evertse and Ferretti.\u0000We study quantitative generalizations and extensions of subspace theorems in various contexts.\u0000We establish a generalization of Evertse and Ferretti’s Absolute Subspace Theorem for hyperplanes in general position.\u0000We obtain improved (non-absolute) Quantitative Subspace Theorems for hyperplanes in general position and in subgeneral position.\u0000We show a Semi-quantitative Subspace Theorem for hyperplanes in non-subdegenerate position.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140977459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we characterize Li–Yorke chaotic composition operators on Orlicz spaces. Indeed, some necessary and sufficient conditions are provided for Li–Yorke chaotic composition operator Cφ{C_{varphi}} on the Orlicz space LΦ(μ){L^{Phi}(mu)}. In some cases we have equivalent conditions for composition operators on Orlicz spaces to be Li–Yorke chaotic. The results of this paper extend similar results in Lp{L^{p}}-spaces.
本文描述了奥利奇空间上的李-约克混沌合成算子的特征。事实上，本文为奥利奇空间 L Φ ( μ ) {L^{Phi}(mu)} 上的李-约克混沌组成算子 C φ {C_{varphi}} 提供了一些必要条件和充分条件。在某些情况下，我们对奥利兹空间上的组成算子具有等效的条件，即 Li-Yorke 混沌算子。本文的结果扩展了 L p {L^{p}} 中的类似结果。 -空间的类似结果。
{"title":"Li–Yorke chaos for composition operators on Orlicz spaces","authors":"Y. Estaremi, Shah Muhammad","doi":"10.1515/forum-2022-0380","DOIUrl":"https://doi.org/10.1515/forum-2022-0380","url":null,"abstract":"\u0000 <jats:p>In this paper we characterize Li–Yorke chaotic composition operators on Orlicz spaces. Indeed, some necessary and sufficient conditions are provided for Li–Yorke chaotic composition operator <jats:inline-formula id=\"j_forum-2022-0380_ineq_9999\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:msub>\u0000 <m:mi>C</m:mi>\u0000 <m:mi>φ</m:mi>\u0000 </m:msub>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2022-0380_eq_0107.png\"/>\u0000 <jats:tex-math>{C_{varphi}}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula> on the Orlicz space <jats:inline-formula id=\"j_forum-2022-0380_ineq_9998\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:msup>\u0000 <m:mi>L</m:mi>\u0000 <m:mi mathvariant=\"normal\">Φ</m:mi>\u0000 </m:msup>\u0000 <m:mo></m:mo>\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:mi>μ</m:mi>\u0000 <m:mo stretchy=\"false\">)</m:mo>\u0000 </m:mrow>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2022-0380_eq_0116.png\"/>\u0000 <jats:tex-math>{L^{Phi}(mu)}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>. In some cases we have equivalent conditions for composition operators on Orlicz spaces to be Li–Yorke chaotic. The results of this paper extend similar results in <jats:inline-formula id=\"j_forum-2022-0380_ineq_9997\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:msup>\u0000 <m:mi>L</m:mi>\u0000 <m:mi>p</m:mi>\u0000 </m:msup>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2022-0380_eq_0118.png\"/>\u0000 <jats:tex-math>{L^{p}}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>-spaces.</jats:p>","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the Moore–Penrose inverse of perturbations by a proper symmetrically-normed ideal of a closed range operator on a Hilbert space. We show that the notion of essential codimension of projections gives a characterization of subsets of such perturbations in which the Moore–Penrose inverse is continuous with respect to the metric induced by the operator ideal. These subsets are maximal satisfying the continuity property, and they carry the structure of real analytic Banach manifolds, which are acted upon transitively by the Banach–Lie group consisting of invertible operators associated with the ideal. This geometric construction allows us to prove that the Moore–Penrose inverse is indeed a real bianalytic map between infinite-dimensional manifolds. We use these results to study the polar decomposition of closed range operators from a similar geometric perspective. At this point we prove that operator monotone functions are real analytic in the norm of any proper symmetrically-normed ideal. Finally, we show that the maps defined by the operator modulus and the polar factor in the polar decomposition of closed range operators are real analytic fiber bundles.
{"title":"Geometric approach to the Moore–Penrose inverse and the polar decomposition of perturbations by operator ideals","authors":"Eduardo Chiumiento, Pedro Massey","doi":"10.1515/forum-2024-0010","DOIUrl":"https://doi.org/10.1515/forum-2024-0010","url":null,"abstract":"We study the Moore–Penrose inverse of perturbations by a proper symmetrically-normed ideal of a closed range operator on a Hilbert space. We show that the notion of essential codimension of projections gives a characterization of subsets of such perturbations in which the Moore–Penrose inverse is continuous with respect to the metric induced by the operator ideal. These subsets are maximal satisfying the continuity property, and they carry the structure of real analytic Banach manifolds, which are acted upon transitively by the Banach–Lie group consisting of invertible operators associated with the ideal. This geometric construction allows us to prove that the Moore–Penrose inverse is indeed a real bianalytic map between infinite-dimensional manifolds. We use these results to study the polar decomposition of closed range operators from a similar geometric perspective. At this point we prove that operator monotone functions are real analytic in the norm of any proper symmetrically-normed ideal. Finally, we show that the maps defined by the operator modulus and the polar factor in the polar decomposition of closed range operators are real analytic fiber bundles.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let p be an odd prime and let ρ:ℤ/p→GLn(ℤ){rho:mathbb{Z}/prightarrowoperatorname{{GL}}_{n}(mathbb{Z})} be an action of ℤ/p{mathbb{Z}/p} on a lattice and let Γ:=ℤn⋊ρℤ/p{Gamma:=mathbb{Z}^{n}rtimes_{rho}mathbb{Z}/p} be the corresponding semidirect product. The torus bundle M:=Tρn×ℤ/pSℓ{M:=T^{n}_{rho}times_{mathbb{Z}/p}S^{ell}} over the lens space Sℓ/ℤ/p{S^{ell}/mathbb{Z}/p} has fundamental group Γ. When
让 p 是奇素数，让 ρ : ℤ / p → GL n ( ℤ ) {rho:mathbb{Z}/prightarrowoperatorname{{GL}}_{n}(mathbb{Z})} } 是 ℤ / p {mathbb{Z}/p} 在网格上的作用，让 Γ ：= ℤ n ⋊ ρ ℤ / p {Gamma:=mathbb{Z}^{n}rtimes_{rho}mathbb{Z}/p} 是相应的半间接积。透镜空间 S ℓ / ℤ / p {S^{ell}/mathbb{Z}/p} 上的环束 M := T ρ n × ℤ / p S ℓ {M:=T^{n}_{rho}times_{mathbb{Z}/p}S^{ell}} 具有基群 Γ。当ℤ / p {mathbb{Z}/p} 只固定了ℤ n {mathbb{Z}^{n} 的原点时｝ Davis 和 Lück (2021) 计算了 L 群 L m 〈 j 〉 ( ℤ [ Γ ] ) {L^{langle jrangle}_{m}(mathbb{Z}[Gamma])} 和结构集 𝒮 geo , s ( M ) {mathcal{S}}^{rm geo},s}(M)} 。在本文中，我们将这些计算扩展到ℤ / p {mathbb{Z}/p} 对ℤ n {mathbb{Z}^{n} 的所有作用。｝ .具体而言，我们计算 L m 〈 j 〉 ( ℤ [ Γ ] ) {L^{langle jrangle}_{m}(mathbb{Z}[Gamma])} 和 𝒮 geo 、s ( M ) {mathcal{S}}^{rm geo},s}(M)} 在 E ¯ Γ {underline{E}Gamma} 有一个非离散奇异集的情况下。
{"title":"Torus bundles over lens spaces","authors":"Oliver H. Wang","doi":"10.1515/forum-2022-0279","DOIUrl":"https://doi.org/10.1515/forum-2022-0279","url":null,"abstract":"Let <jats:italic>p</jats:italic> be an odd prime and let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>ρ</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mrow> <m:mi>ℤ</m:mi> <m:mo>/</m:mo> <m:mi>p</m:mi> </m:mrow> <m:mo>→</m:mo> <m:mrow> <m:msub> <m:mi>GL</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>ℤ</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2022-0279_eq_0655.png\"/> <jats:tex-math>{rho:mathbb{Z}/prightarrowoperatorname{{GL}}_{n}(mathbb{Z})}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be an action of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>ℤ</m:mi> <m:mo>/</m:mo> <m:mi>p</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2022-0279_eq_0555.png\"/> <jats:tex-math>{mathbb{Z}/p}</jats:tex-math> </jats:alternatives> </jats:inline-formula> on a lattice and let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi mathvariant=\"normal\">Γ</m:mi> <m:mo>:=</m:mo> <m:mrow> <m:mrow> <m:msup> <m:mi>ℤ</m:mi> <m:mi>n</m:mi> </m:msup> <m:msub> <m:mo>⋊</m:mo> <m:mi>ρ</m:mi> </m:msub> <m:mi>ℤ</m:mi> </m:mrow> <m:mo>/</m:mo> <m:mi>p</m:mi> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2022-0279_eq_0490.png\"/> <jats:tex-math>{Gamma:=mathbb{Z}^{n}rtimes_{rho}mathbb{Z}/p}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be the corresponding semidirect product. The torus bundle <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>M</m:mi> <m:mo>:=</m:mo> <m:mrow> <m:msubsup> <m:mi>T</m:mi> <m:mi>ρ</m:mi> <m:mi>n</m:mi> </m:msubsup> <m:msub> <m:mo>×</m:mo> <m:mrow> <m:mi>ℤ</m:mi> <m:mo>/</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msub> <m:msup> <m:mi>S</m:mi> <m:mi mathvariant=\"normal\">ℓ</m:mi> </m:msup> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2022-0279_eq_0440.png\"/> <jats:tex-math>{M:=T^{n}_{rho}times_{mathbb{Z}/p}S^{ell}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> over the lens space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msup> <m:mi>S</m:mi> <m:mi mathvariant=\"normal\">ℓ</m:mi> </m:msup> <m:mo>/</m:mo> <m:mi>ℤ</m:mi> <m:mo>/</m:mo> <m:mi>p</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2022-0279_eq_0463.png\"/> <jats:tex-math>{S^{ell}/mathbb{Z}/p}</jats:tex-math> </jats:alternatives> </jats:inline-formula> has fundamental group Γ. When <jats:inline-formula>","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Consider the chiral non-Hermitian random matrix ensemble with parameters n and v, and let (ζi)1≤i≤n{(zeta_{i})_{1leq ileq n}} be its n eigenvalues with positive x-coordinate. In this paper, we establish deviation probabilities and moderate deviation probabilities for the spectral radius (nn+v)12max
考虑参数为 n 和 v 的手性非ermitian 随机矩阵集合，让 ( ζ i ) 1 ≤ i ≤ n {(zeta_{i})_{1leq ileq n}} 为其 x 坐标为正的 n 个特征值。本文建立了频谱半径 ( n n + v ) 的偏差概率和中等偏差概率 1 2 max 1 ≤ i ≤ n | ζ i | 2 {(frac{n}{n+v})^{frac{1}{2}}max_{1leq ileq n}|zeta_{i}|^{2}} 以及 ( n n + v ) 1 2 min 1 ≤ i ≤ n | ζ i | 2 {(frac{n}{n+v})^{frac{1}{2}}min_{1leq ileq n}|zeta_{i}|^{2}}. .
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