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Quarterly Journal of Mathematics最新文献

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Cyclicity and Exponent of Elliptic Curves Modulo p in Arithmetic Progressions 算术级数中 p 模的椭圆曲线的循环性和指数
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-05-24 DOI: 10.1093/qmath/haae029
Peng-Jie Wong
{"title":"Cyclicity and Exponent of Elliptic Curves Modulo p in Arithmetic Progressions","authors":"Peng-Jie Wong","doi":"10.1093/qmath/haae029","DOIUrl":"https://doi.org/10.1093/qmath/haae029","url":null,"abstract":"In this article, we study the cyclicity problem of elliptic curves $E/mathbb{Q}$ modulo primes in a given arithmetic progression. We extend the recent work of Akbal and Güloğlu by proving an unconditional asymptotic for such a cyclicity problem over arithmetic progressions for elliptic curves E, which also presents a generalization of the previous works of Akbary, Cojocaru, M.R. Murty, V.K. Murty and Serre. In addition, we refine the conditional estimates of Akbal and Güloğlu, which gives log-power savings (for small moduli) and consequently improves the work of Cojocaru and M.R. Murty. Moreover, we study the average exponent of E modulo primes in a given arithmetic progression and obtain several conditional and unconditional estimates, extending the previous works of Freiberg, Kim, Kurlberg and Wu.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Existence and Nonexistence of Solutions of Minkowski-Curvature Problems in Exterior Domains 外域闵科夫斯基曲率问题解的存在与不存在
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-05-09 DOI: 10.1093/qmath/haae023
Tianlan Chen, Haiyi Wu
{"title":"Existence and Nonexistence of Solutions of Minkowski-Curvature Problems in Exterior Domains","authors":"Tianlan Chen, Haiyi Wu","doi":"10.1093/qmath/haae023","DOIUrl":"https://doi.org/10.1093/qmath/haae023","url":null,"abstract":"In this paper, we show some nonexistence results of radial solutions for the following Minkowski curvature problems in an exterior domain: $$ begin{cases} -text{div} big(phi(nabla v(x))big)=k(x)f(v(x)), quadquad xinOmega, v=0 text{on} partialOmega, qquadlimlimits_{xrightarrowinfty}v(x)=0 end{cases} $$ for R sufficiently large, where $phi(s)=frac{s}{sqrt{1-s^{2}}}$ for $sin{mathbb R}$ with $s^2lt1,$ $Omega={xin{{mathbb R}^{N}}: |x| gt R}$, $Ngeq3$ is an integer, $|cdot|$ denotes the Euclidean norm on $mathbb{R}^{N}$, R is a positive parameter, $f:mathbb{R}rightarrowmathbb{R}$ is an odd and locally Lipschitz continuous function and $k in C^{1}(mathbb{R}^{+}, mathbb{R}^{+})$ with $mathbb{R}^{+}=(0, +infty)$. We also apply the fixed-point index theory to establish the existence of positive radial solutions of the above problems for R sufficiently small.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Disjoint Dunford–Pettis-Type Properties in Banach Lattices 巴拿赫网格中的邓福德-佩蒂斯（Dunford-Pettis-Type）互不关联特性
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-05-08 DOI: 10.1093/qmath/haae024
Geraldo Botelho, José Lucas P Luiz, Vinícius C C Miranda
{"title":"Disjoint Dunford–Pettis-Type Properties in Banach Lattices","authors":"Geraldo Botelho, José Lucas P Luiz, Vinícius C C Miranda","doi":"10.1093/qmath/haae024","DOIUrl":"https://doi.org/10.1093/qmath/haae024","url":null,"abstract":"New characterizations of the disjoint Dunford–Pettis property of order p (disjoint DPPp) are proved and applied to show that a Banach lattice of cotype p has the disjoint DPPp whenever its dual has this property. The disjoint Dunford–Pettis$^*$ property of order p (disjoint $DP^*P_p$) is thoroughly investigated. Close connections with the positive Schur property of order p, with the disjoint DPPp, with the p-weak $DP^*$ property and with the positive $DP^*$ property of order p are established. In a final section, we study the polynomial versions of the disjoint DPPp and of the disjoint $DP^*P_p$.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 the Coincidence between Campanato Functions and Lipschitz Functions: A New Approach via Elliptic PDES 论坎帕纳托函数与 Lipschitz 函数的重合：通过椭圆 PDES 的新方法
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-05-03 DOI: 10.1093/qmath/haae019
Bo Li, Jinxia Li, Qingze Lin, Tianjun Shen, Chao Zhang
{"title":"On the Coincidence between Campanato Functions and Lipschitz Functions: A New Approach via Elliptic PDES","authors":"Bo Li, Jinxia Li, Qingze Lin, Tianjun Shen, Chao Zhang","doi":"10.1093/qmath/haae019","DOIUrl":"https://doi.org/10.1093/qmath/haae019","url":null,"abstract":"Let $({mathcal{M}},d,mu)$ be the metric measure space with a Dirichlet form $mathscr{E}$. In this paper, we obtain that the Campanato function and the Lipschitz function do always coincide. Our approach is based on the harmonic extension technology, which extends a function u on ${mathcal{M}}$ to its Poisson integral Ptu on ${mathcal{M}}timesmathbb{R}_+$. With this tool in hand, we can utilize the same Carleson measure condition of the Poisson integral to characterize its Campanato/Lipschitz trace, and hence, they are equivalent to each other. This equivalence was previously obtained by Macías–Segovia [Adv. Math., 1979]. However, we provide a new proof, via the boundary value problem for the elliptic equation. This result indicates the famous saying of Stein–Weiss at the beginning of Chapter II in their book [Princeton Mathematical Series, No. 32, 1971].","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Loop Space Decompositions of Moment-Angle Complexes Associated to Flag Complexes 与旗状复合物相关的矩角复合物的环空间分解
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-04-30 DOI: 10.1093/qmath/haae020
Lewis Stanton
{"title":"Loop Space Decompositions of Moment-Angle Complexes Associated to Flag Complexes","authors":"Lewis Stanton","doi":"10.1093/qmath/haae020","DOIUrl":"https://doi.org/10.1093/qmath/haae020","url":null,"abstract":"We prove that the loop space of the moment-angle complex associated with the k-skeleton of a flag complex belongs to the class $mathcal{P}$ of spaces homotopy equivalent to a finite-type product of spheres and loops on simply connected spheres. To do this, a general result showing $mathcal{P}$ is closed under retracts is proved.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Möbius Functions from Automorphic Forms and a Generalized Sarnak’s Conjecture 论来自自动形式的莫比乌斯函数和广义萨尔纳克猜想
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-04-21 DOI: 10.1093/qmath/haae018
Zhining Wei, Shifan Zhao
{"title":"On Möbius Functions from Automorphic Forms and a Generalized Sarnak’s Conjecture","authors":"Zhining Wei, Shifan Zhao","doi":"10.1093/qmath/haae018","DOIUrl":"https://doi.org/10.1093/qmath/haae018","url":null,"abstract":"In this paper, we consider generalized Möbius functions associated with two types of L-functions: Rankin–Selberg L-functions of symmetric powers of distinct holomorphic cusp forms and L-functions derived from Maass cusp forms. We show that these generalized Möbius functions are weakly orthogonal to bounded sequences. As a direct corollary, a generalized Sarnak’s conjecture holds for these two types of Möbius functions.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140629520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Algebraicity of L-values for GSP4 X GL2 and G GSP4 X GL2 和 G 的 L 值代数性
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-04-15 DOI: 10.1093/qmath/haae016
David Loeffler, Óscar Rivero
{"title":"Algebraicity of L-values for GSP4 X GL2 and G","authors":"David Loeffler, Óscar Rivero","doi":"10.1093/qmath/haae016","DOIUrl":"https://doi.org/10.1093/qmath/haae016","url":null,"abstract":"We prove algebraicity results for critical L-values attached to the group ${rm GSp}_4 times {rm GL}_2$, and for Gan–Gross–Prasad periods which are conjecturally related to central L-values for ${rm GSp}_4 times {rm GL}_2 times {rm GL}_2$. Our result for ${rm GSp}_4 times {rm GL}_2$ overlaps substantially with recent results of Morimoto, but our methods are very different; these results will be used in a sequel paper to construct a new p-adic L-function for ${rm GSp}_4 times {rm GL}_2$. The results for Gan–Gross–Prasad periods appear to be new. A key aspect is the computation of certain Archimedean zeta integrals, whose p-adic counterparts are also studied in this note.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A simple construction of potential operators for compensated compactness 补偿紧凑性势算子的简单构造
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-04-11 DOI: 10.1093/qmath/haae008
Bogdan Raiță
{"title":"A simple construction of potential operators for compensated compactness","authors":"Bogdan Raiță","doi":"10.1093/qmath/haae008","DOIUrl":"https://doi.org/10.1093/qmath/haae008","url":null,"abstract":"We give a short proof of the fact that each homogeneous linear differential operator $mathscr{A}$ of constant rank admits a homogeneous potential operator $mathscr{B}$, meaning that $$kermathscr{A}(xi)=mathrm{im,}mathscr{B}(xi) quadtext{for }xiinmathbb{R}^nbackslash{0}.$$ We make some refinements of the original result and some related remarks.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140562206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Higher-degree Artin conjecture 高阶阿尔丁猜想
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-04-05 DOI: 10.1093/qmath/haae012
Olli Järviniemi
{"title":"Higher-degree Artin conjecture","authors":"Olli Järviniemi","doi":"10.1093/qmath/haae012","DOIUrl":"https://doi.org/10.1093/qmath/haae012","url":null,"abstract":"For an algebraic number α we consider the orders of the reductions of α in finite fields. In the case where α is an integer, it is known by the work on Artin’s primitive root conjecture that the order is ‘almost always almost maximal’ assuming the Generalized Riemann Hypothesis (GRH), but unconditional results remain modest. We consider higher-degree variants under GRH. First, we modify an argument of Roskam to settle the case where α and the reduction have degree two. Second, we give a positive lower density result when α is of degree three and the reduction is of degree two. Third, we give higher-rank results in situations where the reductions are of degree two, three, four or six. As an application we give an almost equidistribution result for linear recurrences modulo primes. Finally, we present a general result conditional to GRH and a hypothesis on smooth values of polynomials at prime arguments.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
HKT Manifolds: Hodge Theory, Formality and Balanced Metrics HKT Manifolds：霍奇理论、形式性与平衡度量
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-04-05 DOI: 10.1093/qmath/haae013
Giovanni Gentili, Nicoletta Tardini
{"title":"HKT Manifolds: Hodge Theory, Formality and Balanced Metrics","authors":"Giovanni Gentili, Nicoletta Tardini","doi":"10.1093/qmath/haae013","DOIUrl":"https://doi.org/10.1093/qmath/haae013","url":null,"abstract":"Let $(M,I,J,K,Omega)$ be a compact HKT manifold, and let us denote with $partial$ the conjugate Dolbeault operator with respect to I, $partial_J:=J^{-1}overlinepartial J$, $partial^Lambda:=[partial,Lambda]$, where Λ is the adjoint of $L:=Omegawedge-$. Under suitable assumptions, we study Hodge theory for the complexes $(A^{bullet,0},partial,partial_J)$ and $(A^{bullet,0},partial,partial^Lambda)$ showing a similar behavior to Kähler manifolds. In particular, several relations among the Laplacians, the spaces of harmonic forms and the associated cohomology groups, together with Hard Lefschetz properties, are proved. Moreover, we show that for a compact HKT $mathrm{SL}(n,mathbb{H})$-manifold, the differential graded algebra $(A^{bullet,0},partial)$ is formal and this will lead to an obstruction for the existence of an HKT $mathrm{SL}(n,mathbb{H})$ structure $(I,J,K,Omega)$ on a compact complex manifold (M, I). Finally, balanced HKT structures on solvmanifolds are studied.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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