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Annales Mathematiques du Quebec最新文献

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Certain types of metrics on almost coKähler manifolds 几乎coKähler流形上的某些类型的度量
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-04-15 DOI: 10.1007/s40316-021-00162-w
Devaraja Mallesha Naik, V. Venkatesha, H. Aruna Kumara
{"title":"Certain types of metrics on almost coKähler manifolds","authors":"Devaraja Mallesha Naik,&nbsp;V. Venkatesha,&nbsp;H. Aruna Kumara","doi":"10.1007/s40316-021-00162-w","DOIUrl":"10.1007/s40316-021-00162-w","url":null,"abstract":"<div><p>In this paper, we study an almost coKähler manifold admitting certain metrics such as <span>(*)</span>-Ricci solitons, satisfying the critical point equation (CPE) or Bach flat. First, we consider a coKähler 3-manifold (<i>M</i>, <i>g</i>) admitting a <span>(*)</span>-Ricci soliton (<i>g</i>, <i>X</i>) and we show in this case that either <i>M</i> is locally flat or <i>X</i> is an infinitesimal contact transformation. Next, we study non-coKähler <span>((kappa ,mu ))</span>-almost coKähler metrics as CPE metrics and prove that such a <i>g</i> cannot be a solution of CPE with non-trivial function <i>f</i>. Finally, we prove that a <span>((kappa , mu ))</span>-almost coKähler manifold (<i>M</i>, <i>g</i>) is coKähler if either <i>M</i> admits a divergence free Cotton tensor or the metric <i>g</i> is Bach flat. In contrast to this, we show by a suitable example that there are Bach flat almost coKähler manifolds which are non-coKähler.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 2","pages":"331 - 347"},"PeriodicalIF":0.5,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00162-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49460704","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: 8
A dominated convergence theorem for Eisenstein series Eisenstein级数的一个支配收敛定理
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-03-18 DOI: 10.1007/s40316-021-00157-7
Johann Franke
{"title":"A dominated convergence theorem for Eisenstein series","authors":"Johann Franke","doi":"10.1007/s40316-021-00157-7","DOIUrl":"10.1007/s40316-021-00157-7","url":null,"abstract":"<div><p>Based on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain modular forms in the Eisenstein space. It states that certain rearrangements of the Fourier series will converge very fast near the cusp <span>(tau = 0)</span>. As an application, we consider <i>L</i>-functions associated to products of Eisenstein series and present natural generalized Dirichlet series representations that converge in an expanded half plane.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"45 2","pages":"291 - 320"},"PeriodicalIF":0.5,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00157-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41755877","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: 1
A criterion for transversality of curves and an application to the rational points 曲线横截性的一个判据及其在有理点上的应用
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-03-13 DOI: 10.1007/s40316-021-00161-x
Evelina Viada
{"title":"A criterion for transversality of curves and an application to the rational points","authors":"Evelina Viada","doi":"10.1007/s40316-021-00161-x","DOIUrl":"10.1007/s40316-021-00161-x","url":null,"abstract":"<div><p>We give a criterion for the transversality of a curve embedded in a product of elliptic curves. We then apply our criterion to some explicit classes of curves. The transversality allows us to apply theorems that produce explicit and implementable bounds for the height of the rational points on the curves.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"45 2","pages":"453 - 464"},"PeriodicalIF":0.5,"publicationDate":"2021-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00161-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45803884","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: 1
Smoothing does not give a selection principle for transport equations with bounded autonomous fields 光滑化没有给出自治域有界输运方程的选择原则
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-03-06 DOI: 10.1007/s40316-021-00160-y
Camillo De Lellis, Vikram Giri
{"title":"Smoothing does not give a selection principle for transport equations with bounded autonomous fields","authors":"Camillo De Lellis,&nbsp;Vikram Giri","doi":"10.1007/s40316-021-00160-y","DOIUrl":"10.1007/s40316-021-00160-y","url":null,"abstract":"<div><p>We give an example of a bounded divergence free autonomous vector field in <span>({mathbb {R}}^3)</span> (and of a nonautonomous bounded divergence free vector field in <span>({mathbb {R}}^2)</span>) and of a smooth initial data for which the Cauchy problem for the corresponding transport equation has 2 distinct solutions. We then show that both solutions are limits of classical solutions of transport equations for appropriate smoothings of the vector fields and of the initial data.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 1","pages":"27 - 39"},"PeriodicalIF":0.5,"publicationDate":"2021-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00160-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50457079","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: 3
Smoothing does not give a selection principle for transport equations with bounded autonomous fields 对于有界自治场的输运方程，平滑并不能给出选择原则
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-03-06 DOI: 10.1007/s40316-021-00160-y
Camillo De Lellis, V. Giri
{"title":"Smoothing does not give a selection principle for transport equations with bounded autonomous fields","authors":"Camillo De Lellis, V. Giri","doi":"10.1007/s40316-021-00160-y","DOIUrl":"https://doi.org/10.1007/s40316-021-00160-y","url":null,"abstract":"","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 1","pages":"27 - 39"},"PeriodicalIF":0.5,"publicationDate":"2021-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00160-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52717192","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
Cutting towers of number fields 切割数场的塔
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-02-22 DOI: 10.1007/s40316-021-00156-8
Farshid Hajir, Christian Maire, Ravi Ramakrishna
{"title":"Cutting towers of number fields","authors":"Farshid Hajir,&nbsp;Christian Maire,&nbsp;Ravi Ramakrishna","doi":"10.1007/s40316-021-00156-8","DOIUrl":"10.1007/s40316-021-00156-8","url":null,"abstract":"<div><p>Given a prime <i>p</i>, a number field <span>({K})</span> and a finite set of places <i>S</i> of <span>({K})</span>, let <span>({K}_S)</span> be the maximal pro-<i>p</i> extension of <span>({K})</span> unramified outside <i>S</i>. Using the Golod–Shafarevich criterion one can often show that <span>({K}_S/{K})</span> is infinite. In both the tame and wild cases we construct infinite subextensions with bounded ramification using the refined Golod–Shafarevich criterion. In the tame setting we are able to produce infinite asymptotically good extensions in which infinitely many primes split completely, and in which <i>every</i> prime has Frobenius of finite order, a phenomenon that had been expected by Ihara. We also achieve new records on Martinet constants (root discriminant bounds) in the totally real and totally complex cases.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"45 2","pages":"321 - 345"},"PeriodicalIF":0.5,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00156-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47345050","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: 10
Einstein metrics, conformal curvature, and anti-holomorphic involutions 爱因斯坦度量、共形曲率和反全纯对合
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-02-19 DOI: 10.1007/s40316-020-00154-2
Claude LeBrun
{"title":"Einstein metrics, conformal curvature, and anti-holomorphic involutions","authors":"Claude LeBrun","doi":"10.1007/s40316-020-00154-2","DOIUrl":"10.1007/s40316-020-00154-2","url":null,"abstract":"<div><p>Building on previous results [17, 35], we complete the classification of compact oriented Einstein 4-manifolds with <span>(det (W^+) &gt; 0)</span>. There are, up to diffeomorphism, exactly 15 manifolds that carry such metrics, and, on each of these manifolds, such metrics sweep out exactly one connected component of the corresponding Einstein moduli space.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"45 2","pages":"391 - 405"},"PeriodicalIF":0.5,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-020-00154-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50456146","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
Stark points on elliptic curves via Perrin-Riou’s philosophy 从Perrin Riou哲学看椭圆曲线上的Stark点
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-02-15 DOI: 10.1007/s40316-021-00158-6
Henri Darmon, Alan Lauder
{"title":"Stark points on elliptic curves via Perrin-Riou’s philosophy","authors":"Henri Darmon,&nbsp;Alan Lauder","doi":"10.1007/s40316-021-00158-6","DOIUrl":"10.1007/s40316-021-00158-6","url":null,"abstract":"<div><p>In the early 90’s, Perrin-Riou (Ann Inst Fourier 43(4):945–995, 1993) introduced an important refinement of the Mazur–Swinnerton-Dyer <i>p</i>-adic <i>L</i>-function of an elliptic curve <i>E</i> over <span>(mathbb {Q})</span>, taking values in its <i>p</i>-adic de Rham cohomology. She then formulated a <i>p</i>-adic analogue of the Birch and Swinnerton-Dyer conjecture for this <i>p</i>-adic <i>L</i>-function, in which the formal group logarithms of global points on <i>E</i> make an intriguing appearance. The present work extends Perrin-Riou’s construction to the setting of a Garret–Rankin triple product (<i>f</i>, <i>g</i>, <i>h</i>), where <i>f</i> is a cusp form of weight two attached to <i>E</i> and <i>g</i> and <i>h</i> are classical weight one cusp forms with inverse nebentype characters, corresponding to odd two-dimensional Artin representations <span>(varrho _g)</span> and <span>(varrho _h)</span> respectively. The resulting <i>p</i>-adic Birch and Swinnerton-Dyer conjecture involves the <i>p</i>-adic logarithms of global points on <i>E</i> defined over the field cut out by <span>(varrho _gotimes varrho _h)</span>, in the style of the regulators that arise in Darmon et al. (Forum Math <b>3</b>(e8):95, 2015), and recovers Perrin-Riou’s original conjecture when <i>g</i> and <i>h</i> are Eisenstein series.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 1","pages":"31 - 48"},"PeriodicalIF":0.5,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00158-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49589370","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: 2
On the Robin spectrum for the hemisphere 关于半球的Robin谱
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-01-21 DOI: 10.1007/s40316-021-00155-9
Zeév Rudnick, Igor Wigman
{"title":"On the Robin spectrum for the hemisphere","authors":"Zeév Rudnick,&nbsp;Igor Wigman","doi":"10.1007/s40316-021-00155-9","DOIUrl":"10.1007/s40316-021-00155-9","url":null,"abstract":"<div><p>We study the spectrum of the Laplacian on the hemisphere with Robin boundary conditions. It is found that the eigenvalues fall into small clusters close to the Neumann spectrum, and satisfy a Szegő type limit theorem. Sharp upper and lower bounds for the gaps between the Robin and Neumann eigenvalues are derived, showing in particular that these are unbounded. Further, it is shown that except for a systematic double multiplicity, there are no multiplicities in the spectrum as soon as the Robin parameter is positive, unlike the Neumann case which is highly degenerate. Finally, the limiting spacing distribution of the desymmetrized spectrum is proved to be the delta function at the origin.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 1","pages":"121 - 137"},"PeriodicalIF":0.5,"publicationDate":"2021-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00155-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50502243","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: 7
On abelian (ell )-towers of multigraphs 一个蜜蜂的多图塔
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-01-15 DOI: 10.1007/s40316-020-00152-4
Daniel Vallières
{"title":"On abelian (ell )-towers of multigraphs","authors":"Daniel Vallières","doi":"10.1007/s40316-020-00152-4","DOIUrl":"10.1007/s40316-020-00152-4","url":null,"abstract":"<div><p>We study how the <span>(ell )</span>-adic valuation of the number of spanning trees varies in regular abelian <span>(ell )</span>-towers of multigraphs. We show that for an infinite family of regular abelian <span>(ell )</span>-towers of bouquets, the <span>(ell )</span>-adic valuation of the number of spanning trees behaves similarly to the <span>(ell )</span>-adic valuation of the class numbers in <span>({mathbb {Z}}_{ell })</span>-extensions of number fields.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"45 2","pages":"433 - 452"},"PeriodicalIF":0.5,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-020-00152-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50483148","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: 5
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