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Annales Mathematiques du Quebec最新文献

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A short note on inadmissible coefficients of weight 2 and (2k+1) newforms 关于权的不可容许系数2和（2k+1）新形式的一个注记
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-06-16 DOI: 10.1007/s40316-021-00168-4
Malik Amir, Andreas Hatziiliou
{"title":"A short note on inadmissible coefficients of weight 2 and (2k+1) newforms","authors":"Malik Amir,&nbsp;Andreas Hatziiliou","doi":"10.1007/s40316-021-00168-4","DOIUrl":"10.1007/s40316-021-00168-4","url":null,"abstract":"<div><p>Let <span>(f(z)=q+sum _{nge 2}a(n)q^n)</span> be a weight <i>k</i> normalized newform with integer coefficients and trivial residual mod 2 Galois representation. We extend the results of Amir and Hong in Amir and Hong (On L-functions of modular elliptic curves and certain K3 surfaces, Ramanujan J, 2021) for <span>(k=2)</span> by ruling out or locating all odd prime values <span>(|ell |&lt;100)</span> of their Fourier coefficients <i>a</i>(<i>n</i>) when <i>n</i> satisfies some congruences. We also study the case of odd weights <span>(kge 1)</span> newforms where the nebentypus is given by a quadratic Dirichlet character.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 2","pages":"389 - 402"},"PeriodicalIF":0.5,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00168-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50486708","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
Local (L^p) norms of Schrödinger eigenfunctions on ({mathbb {S}}^2) ｛mathbb｛S｝｝^2上Schrödinger本征函数的局部（L^p）范数
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-06-10 DOI: 10.1007/s40316-021-00167-5
Gabriel Rivière
{"title":"Local (L^p) norms of Schrödinger eigenfunctions on ({mathbb {S}}^2)","authors":"Gabriel Rivière","doi":"10.1007/s40316-021-00167-5","DOIUrl":"10.1007/s40316-021-00167-5","url":null,"abstract":"<div><p>On the canonical 2-sphere and for Schrödinger eigenfunctions, we obtain a simple geometric criterion on the potential under which we can improve, near a given point and for every <span>(pne 6)</span>, Sogge’s estimates by a power of the eigenvalue. This criterion can be formulated in terms of the critical points of the Radon transform of the potential and it is independent of the choice of eigenfunctions.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 1","pages":"93 - 119"},"PeriodicalIF":0.5,"publicationDate":"2021-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00167-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50468647","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
Root number in integer parameter families of elliptic curves 椭圆曲线整数参数族的根数
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-05-28 DOI: 10.1007/s40316-021-00164-8
Julie Desjardins
{"title":"Root number in integer parameter families of elliptic curves","authors":"Julie Desjardins","doi":"10.1007/s40316-021-00164-8","DOIUrl":"10.1007/s40316-021-00164-8","url":null,"abstract":"<div><p>In a previous article [7], the author proves that the value of the root number varies in a non-isotrivial family of elliptic curves indexed by one parameter <i>t</i> running through <span>({mathbb {Q}})</span>. However, a well-known example of Washington has root number <span>(-1)</span> for every fiber when <i>t</i> runs through <span>({mathbb {Z}})</span>. Such examples are rare since, as proven in this paper, the root number of the integer fibers varies for a large class of families of elliptic curves. This result depends on the squarefree conjecture and Chowla’s conjecture, and is unconditional in many cases.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 2","pages":"367 - 387"},"PeriodicalIF":0.5,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00164-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49656022","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
On prime powers in linear recurrence sequences 关于线性递推序列的素数幂。
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-04-18 DOI: 10.1007/s40316-021-00163-9
Japhet Odjoumani, Volker Ziegler
{"title":"On prime powers in linear recurrence sequences","authors":"Japhet Odjoumani,&nbsp;Volker Ziegler","doi":"10.1007/s40316-021-00163-9","DOIUrl":"10.1007/s40316-021-00163-9","url":null,"abstract":"<div><p>In this paper we consider the Diophantine equation <span>(U_n=p^x)</span> where <span>(U_n)</span> is a linear recurrence sequence, <i>p</i> is a prime number, and <i>x</i> is a positive integer. Under some technical hypotheses on <span>(U_n)</span>, we show that, for any <i>p</i> outside of an effectively computable finite set of prime numbers, there exists at most one solution (<i>n</i>, <i>x</i>) to that Diophantine equation. We compute this exceptional set for the Tribonacci sequence and for the Lucas sequence plus one.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 2","pages":"349 - 366"},"PeriodicalIF":0.5,"publicationDate":"2021-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00163-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41151982","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: 1
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
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