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2-Selmer companion modular forms 2-Selmer同伴模形式
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-12 DOI: 10.1007/s40316-025-00262-x
Abhishek, Somnath Jha, Sudhanshu Shekhar
{"title":"2-Selmer companion modular forms","authors":"Abhishek,&nbsp;Somnath Jha,&nbsp;Sudhanshu Shekhar","doi":"10.1007/s40316-025-00262-x","DOIUrl":"10.1007/s40316-025-00262-x","url":null,"abstract":"<div><p>Let <i>N</i> be a positive integer and <i>K</i> be a number field. Suppose that <span>(f_1, f_2in S_k(Gamma _0(N)))</span> are two newforms such that their residual Galois representations at 2 are isomorphic. Let <span>(omega _2:G_{mathbb {Q}}rightarrow {mathbb {Z}}_2^*)</span> be the 2-adic cyclotomic character. Then, under suitable hypotheses, we have shown that for every quadratic character <span>(chi )</span> of <i>K</i> and each critical twist <i>j</i>,  the residual Greenberg 2-Selmer groups of <span>(f_1chi omega _p^{-j})</span> and <span>(f_2chi omega _p^{-j})</span> over <i>K</i> are isomorphic. This generalizes the corresponding result of Mazur–Rubin on 2-Selmer companion elliptic curves. Conversely, if the difference of the residual Greenberg (respectively Bloch–Kato) 2-Selmer ranks of <span>(f_1chi )</span> and <span>(f_2chi )</span> is bounded independent of every quadratic character <span>(chi )</span> of <i>K</i>,  then under suitable hypotheses we have shown that the residual Galois representations at 2 of <span>(f_1)</span> and <span>(f_2)</span> are isomorphic as <span>(G_K)</span>-modules. The corresponding result for elliptic curves was a conjecture of Mazur–Rubin, which was proved by M. Yu.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"557 - 577"},"PeriodicalIF":0.4,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rank-zero quadratic twists in families of elliptic curves with one rational parameter over (mathbb {Q}) 具有一个有理参数的椭圆曲线族中的秩零二次扭转 (mathbb {Q})
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-12 DOI: 10.1007/s40316-025-00253-y
Abhishek Juyal, Mansi Tyagi
{"title":"Rank-zero quadratic twists in families of elliptic curves with one rational parameter over (mathbb {Q})","authors":"Abhishek Juyal,&nbsp;Mansi Tyagi","doi":"10.1007/s40316-025-00253-y","DOIUrl":"10.1007/s40316-025-00253-y","url":null,"abstract":"<div><p>In this article, we construct a family of elliptic curves <span>(E^A: y^2 = (x + A)(x^2 + A^2))</span> with one <span>(2)</span>-torsion point over <span>(mathbb {Q})</span> and prove that there exist infinitely many square-free integers <span>( d )</span> such that the rank of the quadratic twists of <span>( E^A )</span> by <span>( d )</span> is zero. This work is a generalization of the result of M. Xiong: [On positive proportion of rank-zero twists of elliptic curves over <span>({mathbb {Q}})</span>, J Aust Math Soc 98:281–288, (2015)].</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"491 - 501"},"PeriodicalIF":0.4,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explicit count of integral ideals of an imaginary quadratic field 虚二次域的积分理想的显式计数
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-11 DOI: 10.1007/s40316-025-00243-0
Olivier Ramaré
{"title":"Explicit count of integral ideals of an imaginary quadratic field","authors":"Olivier Ramaré","doi":"10.1007/s40316-025-00243-0","DOIUrl":"10.1007/s40316-025-00243-0","url":null,"abstract":"<div><p>We provide explicit bounds for the number of integral ideals of norms at most <i>X</i> in <span>(mathbb {Q}[sqrt{d}])</span> when <span>(d &lt;0)</span> is a fundamental discriminant with an error term of size <span>(mathcal {O}(X^{1/3}))</span>. In particular, we prove that, when <span>(chi )</span> is the non-principal character modulo 3 and <span>(Xge 1)</span>, we have <span>(sum _{nle X}(1!!!1star chi )(n) = frac{pi X}{3sqrt{3}} +mathcal {O}^*(1.94,X^{1/3}))</span>, and that, when <span>(chi )</span> is the non-principal character modulo 4 and <span>(Xge 1)</span>, we have <span>(sum _{nle X}(1!!!1star chi )(n) = frac{pi X}{4} +mathcal {O}^*(1.4,X^{1/3}))</span>. <b>Résumé.</b> Nous dénombrons de façon explicite avec un terme d’erreur <span>(mathcal {O}(X^{1/3}))</span> le nombre d’idéaux entiers de norme au plus <i>X</i> du corps <span>(mathbb {Q}[sqrt{d}])</span> lorsque <span>(d &lt;0)</span> est un discriminant fondamental. Nous montrons en particulier que, lorsque <span>(chi )</span> est le caractère non principal modulo 3 et <span>(Xge 1)</span>, nous avons <span>(sum _{nle X}(1!!!1star chi )(n) = frac{pi X}{3sqrt{3}} +mathcal {O}^*(1.94,X^{1/3}))</span>, et que , lorsque <span>(chi )</span> est le caractère non principal modulo 4 et <span>(Xge 1)</span>, nous avons <span>(sum _{nle X}(1!!!1star chi )(n) = frac{pi X}{4} +mathcal {O}^*(1.4,X^{1/3} ))</span>.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"463 - 475"},"PeriodicalIF":0.4,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Contractible complexes and non-positive immersions 可收缩复合物和非正浸没
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-01-27 DOI: 10.1007/s40316-024-00229-4
William Fisher
{"title":"Contractible complexes and non-positive immersions","authors":"William Fisher","doi":"10.1007/s40316-024-00229-4","DOIUrl":"10.1007/s40316-024-00229-4","url":null,"abstract":"<div><p>We provide examples of contractible complexes which fail to have non-positive immersions and weak non-positive immersions, answering a conjecture of Wise in the negative.\u0000</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"367 - 373"},"PeriodicalIF":0.4,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-024-00229-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Galois codescent for motivic tame kernels 动机驯服核的伽罗瓦代码
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-01-27 DOI: 10.1007/s40316-024-00233-8
J. Assim, A. Movahhedi
{"title":"Galois codescent for motivic tame kernels","authors":"J. Assim,&nbsp;A. Movahhedi","doi":"10.1007/s40316-024-00233-8","DOIUrl":"10.1007/s40316-024-00233-8","url":null,"abstract":"<div><p>Let <i>L</i>/<i>F</i> be a finite Galois extension of number fields with an arbitrary Galois group <i>G</i>. We give an explicit description of the kernel of the natural map on motivic cohomology of the rings of integers <span>(H^2_mathcal {M}(o_L, {textbf{Z}}(i))_{G} {longrightarrow } H^2_mathcal {M}(o_F, {textbf{Z}}(i)))</span>. Using the link between motivic cohomology and <i>K</i>-theory, we deduce genus formulae for all even <i>K</i>-groups <span>(K_{2i-2}(o_F))</span> of the ring of integers. As a by-product, we answer a question raised by B. Kahn about a signature map.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"503 - 555"},"PeriodicalIF":0.4,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Radial limits of solutions to elliptic partial differential equations 椭圆型偏微分方程解的径向极限
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-01-20 DOI: 10.1007/s40316-025-00241-2
Paul M. Gauthier, Mohammad Shirazi
{"title":"Radial limits of solutions to elliptic partial differential equations","authors":"Paul M. Gauthier,&nbsp;Mohammad Shirazi","doi":"10.1007/s40316-025-00241-2","DOIUrl":"10.1007/s40316-025-00241-2","url":null,"abstract":"<div><p>For certain elliptic differential operators <i>L</i>,  we study the behaviour of solutions to <span>(Lu=0,)</span> as we tend to the boundary along radii in strictly starlike domains in <span>(mathbb {R}^n, nge 3.)</span> Analogous results are obtained in other special domains. Our approach involves introducing harmonic line bundles as instances of Brelot harmonic spaces and approximating continuous functions by harmonic functions on appropriate subsets. We are required to approximate on certain closed sets, which is not obvious, since the space of continuous functions on an (unbounded) closed set, endowed with the topology of uniform convergence, is not a topological vector space, though it is both a vector space and a topological space.\u0000</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"375 - 402"},"PeriodicalIF":0.4,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On (Lambda )-submodules with finite index of the plus/minus Selmer group over anticyclotomic ({{,mathrm{mathbb {Z}},}}_{p})-extension at inert primes 抗细胞分裂上正/负Selmer群有限指数的(Lambda ) -子模({{,mathrm{mathbb {Z}},}}_{p}) -在惰性素数上的扩展
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-01-11 DOI: 10.1007/s40316-024-00236-5
Ryota Shii
{"title":"On (Lambda )-submodules with finite index of the plus/minus Selmer group over anticyclotomic ({{,mathrm{mathbb {Z}},}}_{p})-extension at inert primes","authors":"Ryota Shii","doi":"10.1007/s40316-024-00236-5","DOIUrl":"10.1007/s40316-024-00236-5","url":null,"abstract":"<div><p>Let <i>K</i> be an imaginary quadratic field where a prime number <span>(p ge 5)</span> is inert. Let <i>E</i> be an elliptic curve defined over <i>K</i> and suppose that <i>E</i> has good supersingular reduction at <i>p</i>. In this paper, we prove that the plus/minus Selmer group of <i>E</i> over the anticyclotomic <span>({{,mathrm{mathbb {Z}},}}_{p})</span>-extension of <i>K</i> has no proper <span>(Lambda )</span>-submodules of finite index under mild assumptions for <i>E</i>. This is an analogous result to R. Greenberg and B. D. Kim for the anticyclotomic <span>({{,mathrm{mathbb {Z}},}}_{p})</span>-extension essentially. By applying the results of A. Agboola–B. Howard or A. Burungale–K. Büyükboduk–A. Lei, we can also construct examples satisfying the assumptions of our theorem.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"477 - 490"},"PeriodicalIF":0.4,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniqueness of Lagrangians in (T^*{mathbb {R}}P^2) 拉格朗日量的唯一性 (T^*{mathbb {R}}P^2)
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2025-01-11 DOI: 10.1007/s40316-024-00238-3
Nikolas Adaloglou
{"title":"Uniqueness of Lagrangians in (T^*{mathbb {R}}P^2)","authors":"Nikolas Adaloglou","doi":"10.1007/s40316-024-00238-3","DOIUrl":"10.1007/s40316-024-00238-3","url":null,"abstract":"<div><p>We present a new and simpler proof of the fact that any Lagrangian <span>({mathbb {R}}P^2)</span> in <span>(T^*{mathbb {R}}P^2)</span> is Hamiltonian isotopic to the zero section. Our proof mirrors the one given by Li and Wu for the Hamiltonian uniqueness of Lagrangians in <span>(T^*S^2)</span>, using surgery to turn Lagrangian spheres into symplectic ones. The main novel contribution is a detailed proof of the folklore fact that the complement of a symplectic quadric in <span>({mathbb {C}}P^2)</span> can be identified with the unit cotangent disc bundle of <span>({mathbb {R}}P^2)</span>.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"215 - 222"},"PeriodicalIF":0.5,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Closed flat Riemannian 4-manifolds 闭合平坦黎曼4流形
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-01-10 DOI: 10.1007/s40316-024-00231-w
Thomas P. Lambert, John G. Ratcliffe, Steven T. Tschantz
{"title":"Closed flat Riemannian 4-manifolds","authors":"Thomas P. Lambert,&nbsp;John G. Ratcliffe,&nbsp;Steven T. Tschantz","doi":"10.1007/s40316-024-00231-w","DOIUrl":"10.1007/s40316-024-00231-w","url":null,"abstract":"<div><p>In this paper, we describe the classification of all the geometric fibrations of a closed flat Riemannian 4-manifold over a connected 1-orbifold.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"287 - 333"},"PeriodicalIF":0.4,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-024-00231-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some remarks on critical sets of Laplace eigenfunctions 关于拉普拉斯特征函数临界集的若干注记
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2025-01-09 DOI: 10.1007/s40316-024-00240-9
Chris Judge, Sugata Mondal
{"title":"Some remarks on critical sets of Laplace eigenfunctions","authors":"Chris Judge,&nbsp;Sugata Mondal","doi":"10.1007/s40316-024-00240-9","DOIUrl":"10.1007/s40316-024-00240-9","url":null,"abstract":"<p>We study the set of critical points of a solution to <span>(Delta u = lambda cdot u)</span> and in particular components of the critical set that have codimension 1. We show, for example, that if a second Neumann eigenfunction of a simply connected polygon <i>P</i> has infinitely many critical points, then <i>P</i> is a rectangle.</p>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"155 - 163"},"PeriodicalIF":0.5,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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