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Annales Mathematiques du Quebec最新文献

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Volume formula for N-fold reduced products N倍还原产物的体积公式
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-07-30 DOI: 10.1007/s40316-021-00171-9
L. Jeffrey, Jia Ji
{"title":"Volume formula for N-fold reduced products","authors":"L. Jeffrey,&nbsp;Jia Ji","doi":"10.1007/s40316-021-00171-9","DOIUrl":"10.1007/s40316-021-00171-9","url":null,"abstract":"<div><p>Let <i>G</i> be a semisimple compact connected Lie group. An <i>N</i>-fold reduced product of <i>G</i> is the symplectic quotient of the Hamiltonian system of the Cartesian product of <i>N</i> coadjoint orbits of <i>G</i> under diagonal coadjoint action of <i>G</i>. Under appropriate assumptions, it is a symplectic orbifold. Using the technique of nonabelian localization and the residue formula of Jeffrey and Kirwan, we investigate the symplectic volume of an <i>N</i>-fold reduced product of <i>G</i>. Suzuki and Takakura gave a volume formula for the <i>N</i>-fold reduced product of <span>( mathbf {SU}(3) )</span> in [25] by using geometric quantization and the Riemann–Roch formula. We compare our volume formula with theirs and prove that our volume formula agrees with theirs in the case of triple reduced products of <span>( mathbf {SU}(3) )</span>.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 2","pages":"263 - 294"},"PeriodicalIF":0.5,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00171-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50526017","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
Statistical properties of eigenfunctions 本征函数的统计性质
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-07-30 DOI: 10.1007/s40316-021-00170-w
Alexander Shnirelman
{"title":"Statistical properties of eigenfunctions","authors":"Alexander Shnirelman","doi":"10.1007/s40316-021-00170-w","DOIUrl":"10.1007/s40316-021-00170-w","url":null,"abstract":"<div><p>This is a translation of the paper “Статистические  свойства  собственных  функций” which appeared in the Proceedings of the All-USSR School in Differential Equations with Infinite Number of Independent Variables and in Dynamical Systems with Infinitely Many Degrees of Freedom, Dilijan, Armenia, May 21–June 3, 1973; published by the Armenian Academy of Sciences, Yerevan, 1974. Translated from the Russian original by Semyon Dyatlov.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 1","pages":"3 - 9"},"PeriodicalIF":0.5,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00170-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48046673","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: 9
On exceptional zeros of Garrett–Hida p-adic L-functions 关于Garrett–Hida p-adic L-函数的例外零
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-07-01 DOI: 10.1007/s40316-021-00166-6
Massimo Bertolini, Marco Adamo Seveso, Rodolfo Venerucci
{"title":"On exceptional zeros of Garrett–Hida p-adic L-functions","authors":"Massimo Bertolini,&nbsp;Marco Adamo Seveso,&nbsp;Rodolfo Venerucci","doi":"10.1007/s40316-021-00166-6","DOIUrl":"10.1007/s40316-021-00166-6","url":null,"abstract":"<div><p>This article proves a case of the <i>p</i>-adic Birch and Swinnerton-Dyer conjecture for Garrett <i>p</i>-adic <i>L</i>-functions of [6], in the exceptional zero setting of extended analytic rank 2.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 2","pages":"303 - 324"},"PeriodicalIF":0.5,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00166-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43315056","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
Around quantum ergodicity 围绕量子遍历性
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-06-24 DOI: 10.1007/s40316-021-00165-7
Semyon Dyatlov
{"title":"Around quantum ergodicity","authors":"Semyon Dyatlov","doi":"10.1007/s40316-021-00165-7","DOIUrl":"10.1007/s40316-021-00165-7","url":null,"abstract":"<div><p>We discuss Shnirelman’s Quantum Ergodicity Theorem, giving an outline of a proof and an overview of some of the recent developments in mathematical Quantum Chaos.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 1","pages":"11 - 26"},"PeriodicalIF":0.5,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00165-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50510413","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: 6
Algebraicity of the central critical values of twisted triple product L-functions 扭曲三重积l函数中心临界值的代数性质
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2021-06-22 DOI: 10.1007/s40316-021-00169-3
Shih-Yu Chen
{"title":"Algebraicity of the central critical values of twisted triple product L-functions","authors":"Shih-Yu Chen","doi":"10.1007/s40316-021-00169-3","DOIUrl":"10.1007/s40316-021-00169-3","url":null,"abstract":"<div><p>We study the algebraicity of the central critical values of twisted triple product <i>L</i>-functions associated to motivic Hilbert cusp forms over a totally real étale cubic algebra in the totally unbalanced case. The algebraicity is expressed in terms of the cohomological period constructed via the theory of coherent cohomology on quaternionic Shimura varieties developed by Harris. As an application, we generalize our previous result with Cheng on Deligne’s conjecture for certain automorphic <i>L</i>-functions for <span>({text {GL}}_3 times {text {GL}}_2)</span>.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 2","pages":"403 - 442"},"PeriodicalIF":0.5,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40316-021-00169-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46080058","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
A short note on inadmissible coefficients of weight 2 and $$2k+1$$ 2 k + 1 newforms 关于权重2和$$2k+1$$ 2 k + 1新形式的不可接受系数的简短说明
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 \u0000 \u0000 \u0000 \u0000 $$2k+1$$\u0000 \u0000 \u0000 2\u0000 k\u0000 +\u0000 1\u0000 \u0000 \u0000 newforms","authors":"Malik Amir, Andreas Hatziiliou","doi":"10.1007/s40316-021-00168-4","DOIUrl":"https://doi.org/10.1007/s40316-021-00168-4","url":null,"abstract":"","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 1","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":"48985020","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
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
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