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Pacific Journal of Mathematics最新文献

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Connected components of Morse boundaries of graphs of groups 群图的莫尔斯边界的连通分量
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-09-24 DOI: 10.2140/pjm.2022.317.339
Elia Fioravanti, Annette Karrer
{"title":"Connected components of Morse boundaries of graphs of groups","authors":"Elia Fioravanti, Annette Karrer","doi":"10.2140/pjm.2022.317.339","DOIUrl":"https://doi.org/10.2140/pjm.2022.317.339","url":null,"abstract":"Let a finitely generated group $G$ split as a graph of groups. If edge groups are undistorted and do not contribute to the Morse boundary $partial_MG$, we show that every connected component of $partial_MG$ with at least two points originates from the Morse boundary of a vertex group. Under stronger assumptions on the edge groups (such as wideness in the sense of Druc{t}u-Sapir), we show that Morse boundaries of vertex groups are topologically embedded in $partial_MG$.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48988941","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}
引用次数: 1
A coarse geometric expansion of a variant ofArthur’s truncated traces and some applications 阿瑟截断迹的一种变体的粗略几何展开及其一些应用
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-09-21 DOI: 10.2140/pjm.2022.321.193
Hongjie Yu
{"title":"A coarse geometric expansion of a variant of\u0000Arthur’s truncated traces and some applications","authors":"Hongjie Yu","doi":"10.2140/pjm.2022.321.193","DOIUrl":"https://doi.org/10.2140/pjm.2022.321.193","url":null,"abstract":"Let F be a global function field with constant field $mathbb{F}_q$. Let G be a reductive group over $mathbb{F}_q$. We establish a variant of Arthur's truncated kernel for G and for its Lie algebra which generalizes Arthur's original construction. We establish a coarse geometric expansion for our variant truncation. As applications, we consider some existence and uniqueness problems of some cuspidal automorphic representations for the functions field of the projective line $mathbb{P}^1_{mathbb{F}_q}$ with two points of ramifications.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571168","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}
引用次数: 1
Local exterior square and Asai L-functions forGL(n) in odd characteristic 局部外方阵与Asai l -函数forGL(n)的奇特征
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-09-13 DOI: 10.2140/pjm.2023.322.301
Yeongseong Jo
{"title":"Local exterior square and Asai L-functions for\u0000GL(n) in odd characteristic","authors":"Yeongseong Jo","doi":"10.2140/pjm.2023.322.301","DOIUrl":"https://doi.org/10.2140/pjm.2023.322.301","url":null,"abstract":"Let $F$ be a non-archimedean local field of odd characteristic $p>0$. In this paper, we consider local exterior square $L$-functions $L(s,pi,wedge^2)$, Bump-Friedberg $L$-functions $L(s,pi,BF)$, and Asai $L$-functions $L(s,pi,As)$ of an irreducible admissible representation $pi$ of $GL_m(F)$. In particular, we establish that those $L$-functions, via the theory of integral representations, are equal to their corresponding Artin $L$-functions $L(s,wedge^2(phi(pi)))$, $L(s+1/2,phi(pi))L(s,wedge^2(phi(pi)))$, and $L(s,As(phi(pi)))$ of the associated Langlands parameter $phi(pi)$ under the local Langlands correspondence. These are achieved by proving the identity for irreducible supercuspidal representations, exploiting the local to global argument due to Henniart and Lomeli.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45283370","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}
引用次数: 4
A note on the infinite number of exact Lagrangian fillings for spherical spuns 关于球形水刺精确拉格朗日填充数无限的注记
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-09-07 DOI: 10.2140/pjm.2022.317.143
R. Golovko
{"title":"A note on the infinite number of exact Lagrangian fillings for spherical spuns","authors":"R. Golovko","doi":"10.2140/pjm.2022.317.143","DOIUrl":"https://doi.org/10.2140/pjm.2022.317.143","url":null,"abstract":"In this short note we discuss high-dimensional examples of Legendrian submanifolds of the standard contact Euclidean space with an infinite number of exact Lagrangian fillings up to Hamiltonian isotopy. They are obtained from the examples of Casals and Ng by applying to them the spherical spinning construction.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44181021","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}
引用次数: 6
Cohopfian groups and accessible group classes Cohopfian组和可访问的组类
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-08-31 DOI: 10.2140/pjm.2021.312.457
F. Giovanni, M. Trombetti
{"title":"Cohopfian groups and accessible group classes","authors":"F. Giovanni, M. Trombetti","doi":"10.2140/pjm.2021.312.457","DOIUrl":"https://doi.org/10.2140/pjm.2021.312.457","url":null,"abstract":"","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42697804","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}
引用次数: 6
Local Maass forms and Eichler–Selberg relationsfor negative-weight vector-valued mock modular forms 负权向量值模拟模形式的局部Maas形式和Eichler-Selberg关系
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-08-30 DOI: 10.2140/pjm.2023.322.381
Joshua Males, Andreas Mono
{"title":"Local Maass forms and Eichler–Selberg relations\u0000for negative-weight vector-valued mock modular forms","authors":"Joshua Males, Andreas Mono","doi":"10.2140/pjm.2023.322.381","DOIUrl":"https://doi.org/10.2140/pjm.2023.322.381","url":null,"abstract":"By comparing two different evaluations of a modified (`{a} la Borcherds) higher Siegel theta lift on even lattices of signature $(r,s)$, we prove Eichler--Selberg type relations for a wide class of negative weight vector-valued mock modular forms. In doing so, we detail several properties of the lift, as well as showing that it produces an infinite family of local (and locally harmonic) Maa{ss} forms on Grassmanians in certain signatures.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47011639","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}
引用次数: 2
Origamis associated to minimally intersecting filling pairs 与最小相交填充对相关的Origamis
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-08-23 DOI: 10.2140/pjm.2022.317.1
Tarik Aougab, W. Menasco, M. Nieland
{"title":"Origamis associated to minimally intersecting filling pairs","authors":"Tarik Aougab, W. Menasco, M. Nieland","doi":"10.2140/pjm.2022.317.1","DOIUrl":"https://doi.org/10.2140/pjm.2022.317.1","url":null,"abstract":"Let $S_{g}$ denote the closed orientable surface of genus $g$. In joint work with Huang, the first author constructed exponentially-many (in $g$) mapping class group orbits of pairs of simple closed curves whose complement is a single topological disk. Using different techniques, we improve on this result by constructing factorially-many (again in $g$) such orbits. These new orbits are chosen so that the absolute value of the algebraic intersection number is equal to the geometric intersection number, implying that each pair naturally gives rise to an origami. We collect some rudimentary experimental data on the corresponding $SL(2, mathbb{Z})$-orbits and suggest further study and conjectures.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49573527","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}
引用次数: 3
Certain Fourier operators on GL1 and localLanglands gamma functions GL1和localLanglands-gamma函数上的某些傅立叶算子
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-08-08 DOI: 10.2140/pjm.2022.318.339
Dihua Jiang, Zhilin Luo
{"title":"Certain Fourier operators on GL1 and local\u0000Langlands gamma functions","authors":"Dihua Jiang, Zhilin Luo","doi":"10.2140/pjm.2022.318.339","DOIUrl":"https://doi.org/10.2140/pjm.2022.318.339","url":null,"abstract":". For a split reductive group G over a number field k , let ρ be an n -dimensional complex representation of its complex dual group G ∨ ( C ). For any irreducible cuspidal automorphic representation σ of G ( A ), where A is the ring of adeles of k , in [JL21], the authors introduce the ( σ, ρ )-Schwartz space S σ,ρ ( A × ) and ( σ, ρ )-Fourier operator F σ,ρ , and study the ( σ, ρ, ψ )-Poisson summation formula on GL 1 , under the assumption that the local Langlands functoriality holds for the pair ( G, ρ ) at all local places of k , where ψ is a non-trivial additive character of k A . Such general formulae on GL 1 , as a vast generalization of the classical Poisson summation formula, are expected to be responsible for the Langlands conjecture ([ L70]) on global functional equation for the automorphic L -functions L ( s, σ, ρ ). In order to understand such Poisson summation formulae, we continue with [JL21] and develop a further local theory related to the ( σ, ρ )-Schwartz space S σ,ρ ( A × ) and ( σ, ρ )-Fourier operator F σ,ρ . More precisely, over any local field k ν of k , we define distribution kernel functions k σ ν ,ρ,ψ ν ( x ) on GL 1 that represent the ( σ ν , ρ )-Fourier operators F σ ν ,ρ,ψ ν as convolution integral operators, i.e. generalized Hankel transforms, and the local Langlands γ -functions γ ( s, σ ν , ρ, ψ ν ) as Mellin transform of the kernel functions. As a consequence, we show that any local Langlands γ -functions are the gamma functions in the sense of I. and I. Piatetski-Shapiro in [GGPS] and of A. Weil in [W66].","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42077823","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}
引用次数: 3
On a new class of Laguerre–Pólya typefunctions with applications in number theory 关于一类新的Laguerre–Pólya型函数及其在数论中的应用
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-08-04 DOI: 10.2140/pjm.2022.320.177
Ian Wagner
{"title":"On a new class of Laguerre–Pólya type\u0000functions with applications in number theory","authors":"Ian Wagner","doi":"10.2140/pjm.2022.320.177","DOIUrl":"https://doi.org/10.2140/pjm.2022.320.177","url":null,"abstract":". We define a new class of functions, connected to the classical Laguerre-P´olya class, which we call the shifted Laguerre-P´olya class. Recent work of Griffin, Ono, Rolen, and Zagier shows that the Riemann Xi function is in this class. We prove that a function being in this class is equivalent to its Taylor coefficients, once shifted, being a degree d multiplier sequence for every d , which is equivalent to its shifted coefficients satisfying all of the higher Tur´an inequalities. This mirrors a classical result of P´olya and Schur. For each function in this class we show some order derivative satisfies each extended Laguerre inequality. Finally, we discuss some old and new conjectures about iterated inequalities for functions in this class.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48062990","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}
引用次数: 11
Algebraicity of critical values of triple productL-functions in the balanced case 平衡情况下三重积函数临界值的代数性
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-08-04 DOI: 10.2140/pjm.2022.321.73
Shih-Yu Chen
{"title":"Algebraicity of critical values of triple product\u0000L-functions in the balanced case","authors":"Shih-Yu Chen","doi":"10.2140/pjm.2022.321.73","DOIUrl":"https://doi.org/10.2140/pjm.2022.321.73","url":null,"abstract":"The algebraicity of critical values of triple product $L$-functions in the balanced case was proved by Garrett and Harris, under the assumption that the critical points are on the right and away from center of the critical strip. The missing right-half critical points correspond to certain holomorphic Eisenstein series outside the range of absolute convergence. The remaining difficulties are construction of these holomorphic Eisenstein series and verification of the non-vanishing of the corresponding non-archimedean local zeta integrals. In this paper, we address these problems and complement the result of Garrett and Harris to all critical points. As a consequence, we obtain new cases of Deligne's conjecture for symmetric cube $L$-functions of Hilbert modular forms.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47202160","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}
引用次数: 3
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