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Functional equations of algebraic Rankin–Selberg p-adic L-functions 代数Rankin-Selberg p-adic l -函数的泛函方程
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-18 DOI: 10.1007/s40316-025-00250-1
Kâzım Büyükboduk, Manisha Ganguly
{"title":"Functional equations of algebraic Rankin–Selberg p-adic L-functions","authors":"Kâzım Büyükboduk,&nbsp;Manisha Ganguly","doi":"10.1007/s40316-025-00250-1","DOIUrl":"10.1007/s40316-025-00250-1","url":null,"abstract":"<div><p>This article presents an approach to the functional equation for Selmer complexes, which in turn have applications in the Iwasawa theoretic study of Rankin–Selberg products of the Hida and Coleman families. Our treatment establishes the functional equation for algebraic <i>p</i>-adic <i>L</i>-functions (that are given in terms of characteristic ideals of Selmer groups arising as the cohomology of appropriately defined Selmer complexes in degree 2). This is achieved by recovering the characteristic ideal as the determinant of the said Selmer complex, once we prove (under suitable but rather mild hypotheses) that the Selmer complex in question is perfect with amplitude [1, 2], and its cohomology is concentrated in degree-2. The perfectness of these Selmer complexes turns out to be a delicate problem, and the required properties require a study of Tamagawa numbers in families, which may be of independent interest.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"50 1","pages":"93 - 142"},"PeriodicalIF":0.4,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-025-00250-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147865603","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
Polyakov formulas for conical singularities in two dimensions 二维圆锥奇点的Polyakov公式
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-17 DOI: 10.1007/s40316-025-00263-w
Clara L. Aldana, Klaus Kirsten, Julie Rowlett
{"title":"Polyakov formulas for conical singularities in two dimensions","authors":"Clara L. Aldana,&nbsp;Klaus Kirsten,&nbsp;Julie Rowlett","doi":"10.1007/s40316-025-00263-w","DOIUrl":"10.1007/s40316-025-00263-w","url":null,"abstract":"<div><p>We investigate the zeta-regularized determinant and its variation in the presence of conical singularities, boundaries, and corners. For surfaces with isolated conical singularities which may also have one or more smooth boundary components, we demonstrate both a variational Polyakov formula as well as an integrated Polyakov formula for the conformal variation of the Riemannian metric with conformal factors which are smooth up to all singular points and boundary components. We demonstrate the analogous result for curvilinear polygonal domains in surfaces. We then specialize to finite circular sectors and cones and via two independent methods obtain variational Polyakov formulas for the dependence of the determinant on the opening angle. Notably, this requires the conformal factor to be logarithmically singular at the vertex. We further obtain explicit formulas for the determinant for finite circular sectors and cones.\u0000</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"50 1","pages":"35 - 72"},"PeriodicalIF":0.4,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-025-00263-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147865598","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
Boundedness of Forelli Rudin type integral operators on the unit ball of a non singular cone 非奇异锥的单位球上Forelli Rudin型积分算子的有界性
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-16 DOI: 10.1007/s40316-025-00252-z
Abélard Marius Gbir Yarkaï, Jocelyn Gonessa, Faustin Archange Touadéra, Ernest Mada, Francial G. B. Libengue Dobele-Kpoka
{"title":"Boundedness of Forelli Rudin type integral operators on the unit ball of a non singular cone","authors":"Abélard Marius Gbir Yarkaï,&nbsp;Jocelyn Gonessa,&nbsp;Faustin Archange Touadéra,&nbsp;Ernest Mada,&nbsp;Francial G. B. Libengue Dobele-Kpoka","doi":"10.1007/s40316-025-00252-z","DOIUrl":"10.1007/s40316-025-00252-z","url":null,"abstract":"<div><p>We use a new version of Schur’s test to establish the boundedness of Forelli Rudin type integral operators from <span>(L^p)</span> to <span>(L^q)</span> on the unit ball of a non singular cone. Our results allow to extend the boundedness conditions of Bergman projection in the minimal ball obtained by G. Mengotti and E. H. Youssfi [13].\u0000</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"50 1","pages":"185 - 200"},"PeriodicalIF":0.4,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147865605","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
Elliptic curves of conductor (2^m p), quadratic twists, and Watkins’ conjecture 导体的椭圆曲线(2^m p)，二次曲线，和Watkins猜想
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-16 DOI: 10.1007/s40316-025-00249-8
Jeffrey Hatley, Debanjana Kundu
{"title":"Elliptic curves of conductor (2^m p), quadratic twists, and Watkins’ conjecture","authors":"Jeffrey Hatley,&nbsp;Debanjana Kundu","doi":"10.1007/s40316-025-00249-8","DOIUrl":"10.1007/s40316-025-00249-8","url":null,"abstract":"<div><p>Let <span>(textsf{E}/mathbb {Q})</span> be an elliptic curve. By the modularity theorem, it admits a surjection from a modular curve <span>(X_0(N) rightarrow textsf{E})</span>, and the minimal degree among such maps is called the <i>modular degree</i> of <span>(textsf{E})</span>. By the Mordell–Weil Theorem, <span>(textsf{E}(mathbb {Q})simeq mathbb {Z}^r oplus T)</span> for some nonnegative integer <i>r</i> and some finite group <i>T</i>. Watkins’ Conjecture predicts that <span>(2^r)</span> divides the modular degree, thus suggesting an intriguing link between these geometrically- and algebraically-defined invariants. We offer some new cases of Watkins’ Conjecture, specifically for elliptic curves with additive reduction at 2, good reduction outside of at most two odd primes, and a rational point of order two.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"50 1","pages":"143 - 165"},"PeriodicalIF":0.4,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147865604","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 Selmer groups over Greenberg neighbourhoods in the function field case 函数域情况下Greenberg邻域上的Selmer群
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-16 DOI: 10.1007/s40316-025-00261-y
Sohan Ghosh, Jishnu Ray
{"title":"On Selmer groups over Greenberg neighbourhoods in the function field case","authors":"Sohan Ghosh,&nbsp;Jishnu Ray","doi":"10.1007/s40316-025-00261-y","DOIUrl":"10.1007/s40316-025-00261-y","url":null,"abstract":"<div><p>Greenberg studied the variation of Iwasawa invariants across <span>(mathbb {Z}_p)</span>-extensions of a number field <i>F</i>. One of his key ideas was to appropriately topologize the set of all <span>(mathbb {Z}_p)</span>-extensions of <i>F</i>. Sören Kleine refined Greenberg’s topology to investigate the variation of Iwasawa invariants for Selmer groups of abelian varieties over <span>(mathbb {Z}_p)</span>-extensions of number fields, providing bounds on their <span>(mu )</span>-and <span>(lambda )</span>-invariants. In this article, we adapt Kleine’s techniques to the context of function fields. Specifically, we generalize the application of topology to analyze the variation of Iwasawa invariants associated with Selmer groups over <span>(mathbb {Z}_p)</span>- and <span>(mathbb {Z}_ell )</span>-extensions of function fields.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"50 1","pages":"277 - 293"},"PeriodicalIF":0.4,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147865567","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
Hodge Laplacian Eigenvalues on Surfaces with Boundary 有边界曲面上的霍奇拉普拉斯特征值
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-09-13 DOI: 10.1007/s40316-025-00260-z
Mikhail Muravyev
{"title":"Hodge Laplacian Eigenvalues on Surfaces with Boundary","authors":"Mikhail Muravyev","doi":"10.1007/s40316-025-00260-z","DOIUrl":"10.1007/s40316-025-00260-z","url":null,"abstract":"<div><p>Recently Rohleder proposed a new variational approach to an inequality between the Neumann and Dirichlet eigenvalues in the simply connected planar case using the language of classical vector analysis. Interpreting his approach in terms of differential forms permits to generalize these results to a much broader context. The spectrum of the absolute boundary problem for the Hodge Laplacian on a Riemannian manifold with boundary is the union of the spectra of the absolute boundary problem on the spaces of closed and co-exact forms. An inequality for the eigenvalues of the absolute boundary problem for the Hodge Laplacian and the Dirichlet boundary problem for the Laplace–Beltrami operator in the Euclidean case is obtained using this representation. Rohleder’s results are obtained as corollaries of a more general theorem.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"50 1","pages":"73 - 92"},"PeriodicalIF":0.4,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147865602","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
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