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Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation 三维二次Zakharov-Kuznetsov方程孤立波的渐近稳定性
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2023-11-29 DOI: 10.1353/ajm.2023.a913295
Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko, Kai Yang
{"title":"Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation","authors":"Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko, Kai Yang","doi":"10.1353/ajm.2023.a913295","DOIUrl":"https://doi.org/10.1353/ajm.2023.a913295","url":null,"abstract":"<p><p>Abstract:</p><p>We consider the quadratic Zakharov-Kuznetsov equation $$partial_t u + partial_x Delta u + partial_x u^2=0$$ on $Bbb{R}^3$. A solitary wave solution is given by $Q(x-t,y,z)$, where $Q$ is the ground state solution to $-Q+Delta Q+Q^2=0$. We prove the asymptotic stability of these solitary wave solutions. Specifically, we show that initial data close to $Q$ in the energy space, evolves to a solution that, as $ttoinfty$, converges to a rescaling and shift of $Q(x-t,y,z)$ in $L^2$ in a rightward shifting region $x&gt;delta t-tanthetasqrt{y^2+z^2}$ for $0leqthetaleq{piover 3}-delta$.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"192 11","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Derived Hecke action at p and the ordinary p-adic cohomology of arithmetic manifolds 推导了算术流形在p点的Hecke作用和普通p进上同调
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2023-11-29 DOI: 10.1353/ajm.2023.a913294
Chandrashekhar Khare, Niccoló Ronchetti
{"title":"Derived Hecke action at p and the ordinary p-adic cohomology of arithmetic manifolds","authors":"Chandrashekhar Khare, Niccoló Ronchetti","doi":"10.1353/ajm.2023.a913294","DOIUrl":"https://doi.org/10.1353/ajm.2023.a913294","url":null,"abstract":"<p><p>Abstract:</p><p>We study the derived Hecke action at $p$ on the ordinary $p$-adic cohomology of arithmetic subgroups of reductive groups ${rm G}(Bbb{Q})$. This is the analog at $ell=p$ of derived Hecke actions studied by Venkatesh in the tame case, and is the derived analog of Hida's theory for ordinary Hecke algebras. We show that properties of the derived Hecke action at $p$ are related to deep conjectures in Galois cohomology which are higher analogs of the classical Leopoldt conjecture.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"192 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Scarcity of congruences for the partition function 配分函数的同余的稀缺性
1区 数学
American Journal of Mathematics Pub Date : 2023-10-01 DOI: 10.1353/ajm.2023.a907704
Scott Ahlgren, Olivia Beckwith, Martin Raum
{"title":"Scarcity of congruences for the partition function","authors":"Scott Ahlgren, Olivia Beckwith, Martin Raum","doi":"10.1353/ajm.2023.a907704","DOIUrl":"https://doi.org/10.1353/ajm.2023.a907704","url":null,"abstract":"abstract: The arithmetic properties of the ordinary partition function $p(n)$ have been the topic of intensive study for the past century. Ramanujan proved that there are linear congruences of the form $p(ell n+beta)equiv 0$ $({rm mod};ell)$ for the primes $ell=5,7,11$, and it is known that there are no others of this form. On the other hand, for every prime $ellgeq 5$ there are infinitely many examples of congruences of the form $p(ell Q^m n+beta)equiv 0$ $({rm mod};ell)$ where $Qgeq 5$ is prime and $mgeq 3$. This leaves open the question of the existence of such congruences when $m=1$ or $m=2$ (no examples in these cases are known). We prove in a precise sense that such congruences, if they exist, are exceedingly scarce. Our methods involve a careful study of modular forms of half integral weight on the full modular group which are related to the partition function. Among many other tools, we use work of Radu which describes expansions of such modular forms along square classes at cusps of the modular curve $X(ell Q)$, Galois representations and the arithmetic large sieve.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135996630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 10
The Sn -equivariant top weight Euler characteristic of Mg,n Mg,n .的Sn等变顶重欧拉特性
1区 数学
American Journal of Mathematics Pub Date : 2023-10-01 DOI: 10.1353/ajm.2023.a907705
Melody Chan, Carel Faber, Søren Galatius, Sam Payne
{"title":"The Sn -equivariant top weight Euler characteristic of Mg,n","authors":"Melody Chan, Carel Faber, Søren Galatius, Sam Payne","doi":"10.1353/ajm.2023.a907705","DOIUrl":"https://doi.org/10.1353/ajm.2023.a907705","url":null,"abstract":"abstract: We prove a formula, conjectured by Zagier, for the $S_n$-equivariant Euler characteristic of the top weight cohomology of $scr{M}_{g,n}$.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"284 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135324817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 8
Graded quotients of ramification groups of local fields with imperfect residue fields 具有不完全残域的局部域分支群的梯度商
1区 数学
American Journal of Mathematics Pub Date : 2023-10-01 DOI: 10.1353/ajm.2023.a907702
Takeshi Saito
{"title":"Graded quotients of ramification groups of local fields with imperfect residue fields","authors":"Takeshi Saito","doi":"10.1353/ajm.2023.a907702","DOIUrl":"https://doi.org/10.1353/ajm.2023.a907702","url":null,"abstract":"abstract: We prove that the graded quotients of the filtration by ramification groups of any henselian discrete valuation field of residue characteristic $p&gt;0$ are ${bf F}_p$-vector spaces. We define an injection of the character group of each graded quotient to a twisted cotangent space defined using a cotangent complex.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135324818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 5
Almost representations of algebras and quantization 代数的概表示和量子化
1区 数学
American Journal of Mathematics Pub Date : 2023-10-01 DOI: 10.1353/ajm.2023.a907706
Louis Ioos, David Kazhdan, Leonid Polterovich
{"title":"Almost representations of algebras and quantization","authors":"Louis Ioos, David Kazhdan, Leonid Polterovich","doi":"10.1353/ajm.2023.a907706","DOIUrl":"https://doi.org/10.1353/ajm.2023.a907706","url":null,"abstract":"abstract: We introduce the notion of almost representations of Lie algebras and quantum tori, and establish an Ulam-stability type phenomenon: every irreducible almost representation is close to a genuine irreducible representation. As an application, we prove that geometric quantizations of the two-dimensional sphere and the two-dimensional torus are conjugate in the semi-classical limit up to a small error.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135996629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
On the Mazur-Tate conjecture for prime conductor and Mazur's Eisenstein ideal 论主导体的马祖尔-塔特猜想和马祖尔的爱森斯坦理想
1区 数学
American Journal of Mathematics Pub Date : 2023-10-01 DOI: 10.1353/ajm.2023.a907701
Emmanuel Lecouturier
{"title":"On the Mazur-Tate conjecture for prime conductor and Mazur's Eisenstein ideal","authors":"Emmanuel Lecouturier","doi":"10.1353/ajm.2023.a907701","DOIUrl":"https://doi.org/10.1353/ajm.2023.a907701","url":null,"abstract":"abstract: In 1995, Ehud de Shalit proved an analogue of a conjecture of Mazur-Tate for the modular Jacobian $J_0(p)$. His main result was valid away from the Eisenstein primes. We complete the work of de Shalit by including the Eisenstein primes, and give some applications such as an elementary combinatorial identity involving discrete logarithms of difference of supersingular $j$-invariants. An important tool is our recent work on the so called ``generalized cuspidal $1$-motive''.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135948525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
On weakly turbulent solutions to the perturbed linear harmonic oscillator 摄动线性谐振子的弱湍流解
1区 数学
American Journal of Mathematics Pub Date : 2023-10-01 DOI: 10.1353/ajm.2023.a907703
Erwan Faou, Pierre Raphaël
{"title":"On weakly turbulent solutions to the perturbed linear harmonic oscillator","authors":"Erwan Faou, Pierre Raphaël","doi":"10.1353/ajm.2023.a907703","DOIUrl":"https://doi.org/10.1353/ajm.2023.a907703","url":null,"abstract":"abstract: We introduce specific solutions to the linear harmonic oscillator, named bubbles. They form resonant families of invariant tori of the linear dynamics, with arbitrarily large Sobolev norms. We use these modulated bubbles of energy to construct a class of potentials which are real, smooth, time dependent and uniformly decaying to zero with respect to time, such that the corresponding perturbed quantum harmonic oscillator admits solutions which exhibit a logarithmic growth of Sobolev norms. The resonance mechanism is explicit in space variables and produces highly oscillatory solutions. We then give several recipes to construct similar examples using more specific tools based on the continuous resonant (CR) equation in dimension two.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136119316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 16
Proper proximality in non-positive curvature 非正曲率的适当近距离
1区 数学
American Journal of Mathematics Pub Date : 2023-10-01 DOI: 10.1353/ajm.2023.a907700
Camille Horbez, Jingyin Huang, Jean Lécureux
{"title":"Proper proximality in non-positive curvature","authors":"Camille Horbez, Jingyin Huang, Jean Lécureux","doi":"10.1353/ajm.2023.a907700","DOIUrl":"https://doi.org/10.1353/ajm.2023.a907700","url":null,"abstract":"abstract: Proper proximality of a countable group is a notion that was introduced by Boutonnet, Ioana and Peterson as a tool to study rigidity properties of certain von Neumann algebras associated to groups or ergodic group actions. In the present paper, we establish the proper proximality of many groups acting on nonpositively curved spaces. First, these include many countable groups $G$ acting properly nonelementarily by isometries on a proper ${rm CAT}(0)$ space $X$. More precisely, proper proximality holds in the presence of rank one isometries or when $X$ is a locally thick affine building with a minimal $G$-action. As a consequence of Rank Rigidity, we derive the proper proximality of all countable nonelementary ${rm CAT}(0)$ cubical groups, and of all countable groups acting properly cocompactly nonelementarily by isometries on either a Hadamard manifold with no Euclidean factor, or on a $2$-dimensional piecewise Euclidean ${rm CAT}(0)$ simplicial complex. Second, we establish the proper proximality of many hierarchically hyperbolic groups. These include the mapping class groups of connected orientable finite-type boundaryless surfaces (apart from a few low-complexity cases), thus answering a question raised by Boutonnet, Ioana, and Peterson. We also prove the proper proximality of all subgroups acting nonelementarily on the curve graph. In view of work of Boutonnet, Ioana and Peterson, our results have applications to structural and rigidity results for von Neumann algebras associated to all the above groups and their ergodic actions.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135948778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 7
Automorphic descent for symplectic groups: The branching problems and L-functions 辛群的自同构下降:分支问题与l -函数
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2023-05-31 DOI: 10.1353/ajm.2023.a897497
Baiying Liu, Bin Xu
{"title":"Automorphic descent for symplectic groups: The branching problems and L-functions","authors":"Baiying Liu, Bin Xu","doi":"10.1353/ajm.2023.a897497","DOIUrl":"https://doi.org/10.1353/ajm.2023.a897497","url":null,"abstract":"abstract:We study certain automorphic descent constructions for symplectic groups, and obtain results related to branching problems of automorphic representations. As a byproduct of the construction, based on the knowledge of the global Vogan packets for ${rm Mp}_2(Bbb{A})$, we give a new approach to prove the result that for an automorphic cuspidal representation of ${rm GL}_2(Bbb{A})$ of symplectic type, if there exists a quadratic twist with positive root number, then there exist quadratic twists with non-zero central $L$-values.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"145 1","pages":"807 - 859"},"PeriodicalIF":1.7,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45855106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
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