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Symplectically self-polar polytopes of minimal capacity 最小容量的辛自极性多面体
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-23 DOI: 10.1007/s40316-025-00251-0
Mark Berezovik
{"title":"Symplectically self-polar polytopes of minimal capacity","authors":"Mark Berezovik","doi":"10.1007/s40316-025-00251-0","DOIUrl":"10.1007/s40316-025-00251-0","url":null,"abstract":"<div><p>In this paper we continue the study of symplectically self-polar convex bodies started in [3]. We construct symplectically self-polar convex bodies of the minimal Ekeland–Hofer–Zehnder capacity. This in turn proves that the lower bound for the Ekeland–Hofer–Zehnder capacity for centrally symmetric convex bodies obtained in [1] cannot be improved. We also make some numerical experiments and speculations regarding the minimal volume of symplectically self-polar convex bodies.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"335 - 353"},"PeriodicalIF":0.4,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-025-00251-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223713","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
Eigenvalue bounds for the Steklov problem on differential forms in warped product manifolds 弯曲积流形中微分形式上Steklov问题的特征值界
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-18 DOI: 10.1007/s40316-025-00255-w
Tirumala Chakradhar
{"title":"Eigenvalue bounds for the Steklov problem on differential forms in warped product manifolds","authors":"Tirumala Chakradhar","doi":"10.1007/s40316-025-00255-w","DOIUrl":"10.1007/s40316-025-00255-w","url":null,"abstract":"<div><p>We consider the Steklov problem on differential <span>(ptext {-})</span>forms defined by Karpukhin and present geometric eigenvalue bounds in the setting of warped product manifolds in various scenarios. In particular, we obtain Escobar type lower bounds for warped product manifolds with non-negative Ricci curvature and strictly convex boundary, and certain sharp bounds for hypersurfaces of revolution, among others. We compare and contrast the behaviour with known results in the case of functions (i.e., <span>(0text {-})</span>forms), highlighting the influence of the underlying topology on the spectrum for <span>(ptext {-})</span>forms in general.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"421 - 443"},"PeriodicalIF":0.4,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-025-00255-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223720","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
Two disks maximize the third Robin eigenvalue: positive parameters 两个磁盘使第三个Robin特征值最大化：正参数
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-17 DOI: 10.1007/s40316-025-00254-x
Hanna N. Kim, Richard S. Laugesen
{"title":"Two disks maximize the third Robin eigenvalue: positive parameters","authors":"Hanna N. Kim,&nbsp;Richard S. Laugesen","doi":"10.1007/s40316-025-00254-x","DOIUrl":"10.1007/s40316-025-00254-x","url":null,"abstract":"<div><p>The third eigenvalue of the Robin Laplacian on a simply-connected planar domain of given area is bounded above by the corresponding eigenvalue of a disjoint union of two equal disks, for Robin parameters in <span>([-4pi ,4pi ].)</span> This sharp inequality was known previously only for negative parameters in <span>([-4pi ,0],)</span> by Girouard and Laugesen. Their proof fails for positive Robin parameters because the second eigenfunction on a disk has non-monotonic radial part. This difficulty is overcome for parameters in <span>((0,4pi ])</span> by means of a degree-theoretic approach suggested by Karpukhin and Stern that yields suitably orthogonal trial functions.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"403 - 419"},"PeriodicalIF":0.4,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223723","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
An analogue of Ganea’s theorem for connected sums 关于连通和的Ganea定理的类比
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-15 DOI: 10.1007/s40316-025-00245-y
Stephen Theriault
{"title":"An analogue of Ganea’s theorem for connected sums","authors":"Stephen Theriault","doi":"10.1007/s40316-025-00245-y","DOIUrl":"10.1007/s40316-025-00245-y","url":null,"abstract":"<div><p>Let <i>M</i> and <i>N</i> be simply-connected <i>n</i>-dimensional Poincaré Duality complexes. A condition is given on <i>M</i> and <i>N</i> which allows for the based loops on the connected sum <span>(M#N)</span> to be expressed as a product of the based loops on <i>M</i>, the based loops on <i>N</i>, and an explicitly identified complementary factor. This is analogous to Ganea’s decomposition of the based loops on a wedge. A generalization is given for a connected sum of <i>k</i> Poincaré Duality complexes for any <span>(kge 2)</span>. The required condition holds, for instance, for products of spheres. Examples are given that are of particular interest in toric topology.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"355 - 366"},"PeriodicalIF":0.4,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-025-00245-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223721","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
Linear independence of periods for the symmetric square L-functions 对称方形l函数周期的线性无关性
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-13 DOI: 10.1007/s40316-025-00258-7
Tianyu Ni, Hui Xue
{"title":"Linear independence of periods for the symmetric square L-functions","authors":"Tianyu Ni,&nbsp;Hui Xue","doi":"10.1007/s40316-025-00258-7","DOIUrl":"10.1007/s40316-025-00258-7","url":null,"abstract":"<div><p>For <span>(S_k)</span>, the space of cusp forms of weight <i>k</i> for the full modular group, we first introduce periods on <span>(S_k)</span> associated to symmetric square <i>L</i>-functions. We then prove that for a fixed natural number <i>n</i>, if <i>k</i> is sufficiently large relative to <i>n</i>, then any <i>n</i> such periods are linearly independent. With some extra assumption, we also prove that for <span>(kge e^{12})</span>, we can always pick up to <span>(frac{log k}{4})</span> arbitrary linearly independent periods.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"445 - 462"},"PeriodicalIF":0.4,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223722","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
The capitulation problem in certain pure cubic fields 纯立方场中的投降问题
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-12 DOI: 10.1007/s40316-025-00248-9
Siham Aouissi, Daniel C. Mayer
{"title":"The capitulation problem in certain pure cubic fields","authors":"Siham Aouissi,&nbsp;Daniel C. Mayer","doi":"10.1007/s40316-025-00248-9","DOIUrl":"10.1007/s40316-025-00248-9","url":null,"abstract":"<div><p>Let <span>(Gamma ={mathbb {Q}}(root 3 of {n}))</span> be a pure cubic field with normal closure <span>(k={mathbb {Q}}(root 3 of {n},zeta ),)</span> where <span>(n&gt;1)</span> denotes a cube free integer, and <span>(zeta )</span> is a primitive cube root of unity. Suppose <i>k</i> possesses an elementary bicyclic 3-class group <span>({textrm{Cl}}_3(k),)</span> and the conductor of <span>(k/{mathbb {Q}}(zeta ))</span> has the shape <span>(fin lbrace pq_1q_2,3pq,9pqrbrace )</span> where <span>(pequiv 1,({textrm{mod}},9))</span> and <span>(q,q_1,q_2equiv 2,5,({textrm{mod}},9))</span> are primes. It is disproved that there are only two possible capitulation types <span>(varkappa (k),)</span> either type <span>({textrm{a}}.1,)</span> (0000),  or type <span>({textrm{a}}.2,)</span> (1000). Evidence is provided, theoretically and experimentally, of two further types, <span>({text {b}}.10,)</span> (0320),  and <span>({textrm{d}}.23,)</span> (1320).</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"579 - 597"},"PeriodicalIF":0.4,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223711","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
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
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