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Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

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Arithmetic of Catalan’s constant and its relatives 加泰隆常数及其相关常数的计算
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-05-27 DOI: 10.1007/s12188-019-00203-w
Wadim Zudilin
{"title":"Arithmetic of Catalan’s constant and its relatives","authors":"Wadim Zudilin","doi":"10.1007/s12188-019-00203-w","DOIUrl":"10.1007/s12188-019-00203-w","url":null,"abstract":"<div><p>We prove that at least one of the six numbers <span>(beta (2i))</span> for <span>(i=1,ldots ,6)</span> is irrational. Here <span>(beta (s)=sum _{k=0}^{infty }(-1)^k(2k+1)^{-s})</span> denotes Dirichlet’s beta function, so that <span>(beta (2))</span> is Catalan’s constant.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"89 1","pages":"45 - 53"},"PeriodicalIF":0.4,"publicationDate":"2019-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00203-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50049895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
One-line formula for automorphic differential operators on Siegel modular forms Siegel模形式上自同构微分算子的单线公式
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-04-27 DOI: 10.1007/s12188-019-00202-x
Tomoyoshi Ibukiyama
{"title":"One-line formula for automorphic differential operators on Siegel modular forms","authors":"Tomoyoshi Ibukiyama","doi":"10.1007/s12188-019-00202-x","DOIUrl":"10.1007/s12188-019-00202-x","url":null,"abstract":"<div><p>We consider the Siegel upper half space <span>(H_{2m})</span> of degree 2<i>m</i> and a subset <span>(H_mtimes H_m)</span> of <span>(H_{2m})</span> consisting of two <span>(mtimes m)</span> diagonal block matrices. We consider two actions of <span>(Sp(m,{mathbb R})times Sp(m,{mathbb R}) subset Sp(2m,{mathbb R}))</span>, one is the action on holomorphic functions on <span>(H_{2m})</span> defined by the automorphy factor of weight <i>k</i> on <span>(H_{2m})</span> and the other is the action on vector valued holomorphic functions on <span>(H_mtimes H_m)</span> defined on each component by automorphy factors obtained by <span>(det^k otimes rho )</span>, where <span>(rho )</span> is a polynomial representation of <span>(GL(n,{mathbb C}))</span>. We consider vector valued linear holomorphic differential operators with constant coefficients on holomorphic functions on <span>(H_{2m})</span> which give an equivariant map with respect to the above two actions under the restriction to <span>(H_mtimes H_m)</span>. In a previous paper, we have already shown that all such operators can be obtained either by a projection of the universal automorphic differential operator or alternatively by a vector of <i>monomial basis</i> corresponding to the partition <span>(2m=m+m)</span>. Here in this paper, based on a completely different idea, we give much simpler looking one-line formula for such operators. This is obtained independently from our previous results. The proofs also provide more algorithmic approach to our operators.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"89 1","pages":"17 - 43"},"PeriodicalIF":0.4,"publicationDate":"2019-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00202-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50049322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
The uniqueness of Weierstrass points with semigroup (langle a;brangle ) and related semigroups 具有半群(langle a;brangle )及相关半群的Weierstrass点的唯一性
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-02-15 DOI: 10.1007/s12188-019-00201-y
Marc Coppens
{"title":"The uniqueness of Weierstrass points with semigroup (langle a;brangle ) and related semigroups","authors":"Marc Coppens","doi":"10.1007/s12188-019-00201-y","DOIUrl":"10.1007/s12188-019-00201-y","url":null,"abstract":"<div><p>Assume <i>a</i> and <span>(b=na+r)</span> with <span>(n ge 1)</span> and <span>(0&lt;r&lt;a)</span> are relatively prime integers. In case <i>C</i> is a smooth curve and <i>P</i> is a point on <i>C</i> with Weierstrass semigroup equal to <span>(&lt;a;b&gt;)</span> then <i>C</i> is called a <span>(C_{a;b})</span>-curve. In case <span>(r ne a-1)</span> and <span>(b ne a+1)</span> we prove <i>C</i> has no other point <span>(Q ne P)</span> having Weierstrass semigroup equal to <span>(&lt;a;b&gt;)</span>, in which case we say that the Weierstrass semigroup <span>(&lt;a;b&gt;)</span> occurs at most once. The curve <span>(C_{a;b})</span> has genus <span>((a-1)(b-1)/2)</span> and the result is generalized to genus <span>(g&lt;(a-1)(b-1)/2)</span>. We obtain a lower bound on <i>g</i> (sharp in many cases) such that all Weierstrass semigroups of genus <i>g</i> containing <span>(&lt;a;b&gt;)</span> occur at most once.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"89 1","pages":"1 - 16"},"PeriodicalIF":0.4,"publicationDate":"2019-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00201-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50053183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Functional equations of real analytic Jacobi Eisenstein series 实解析Jacobi Eisenstein级数的泛函方程
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-01-14 DOI: 10.1007/s12188-019-00200-z
Shin-ichiro Mizumoto
{"title":"Functional equations of real analytic Jacobi Eisenstein series","authors":"Shin-ichiro Mizumoto","doi":"10.1007/s12188-019-00200-z","DOIUrl":"10.1007/s12188-019-00200-z","url":null,"abstract":"<div><p>We prove the existence of meromorphic continuation and the functional equation of the real analytic Jacobi Eisenstein series of degree <i>m</i> and matrix index <i>T</i> in case <i>T</i> is a kernel form.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"89 1","pages":"55 - 75"},"PeriodicalIF":0.4,"publicationDate":"2019-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00200-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50024885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On linear relations for L-values over real quadratic fields 关于实二次域上l值的线性关系
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-11-22 DOI: 10.1007/s12188-018-0199-4
Ren-He Su
{"title":"On linear relations for L-values over real quadratic fields","authors":"Ren-He Su","doi":"10.1007/s12188-018-0199-4","DOIUrl":"10.1007/s12188-018-0199-4","url":null,"abstract":"<div><p>In this paper, we give a method to construct a classical modular form from a Hilbert modular form. By applying this method, we can get linear formulas which relate the Fourier coefficients of the Hilbert and classical modular forms. The paper focuses on the Hilbert modular forms over real quadratic fields. We will state a construction of relations between the special values of L-functions, especially at 0, and arithmetic functions. We will also give a relation between the sum of squares functions with underlying fields <span>(mathbb {Q}(sqrt{D}))</span> and <span>(mathbb {Q})</span>.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 2","pages":"317 - 330"},"PeriodicalIF":0.4,"publicationDate":"2018-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0199-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50042983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A motivic study of generalized Burniat surfaces 广义燃烧曲面的动力学研究
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-11-01 DOI: 10.1007/s12188-018-0198-5
Chris Peters
{"title":"A motivic study of generalized Burniat surfaces","authors":"Chris Peters","doi":"10.1007/s12188-018-0198-5","DOIUrl":"10.1007/s12188-018-0198-5","url":null,"abstract":"<div><p>Generalized Burniat surfaces are surfaces of general type with <span>(p_g=q)</span> and Euler number <span>(e=6)</span> obtained by a variant of Inoue’s construction method for the classical Burniat surfaces. I prove a variant of the Bloch conjecture for these surfaces. The method applies also to the so-called Sicilian surfaces introduced by Bauer et al. in (J Math Sci Univ Tokyo 22(2–15):55–111, 2015. arXiv:1409.1285v2). This implies that the Chow motives of all of these surfaces are finite-dimensional in the sense of Kimura.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 2","pages":"377 - 387"},"PeriodicalIF":0.4,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0198-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50000234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Modular forms for the (A_{1})-tower (A_{1}) -塔的模块化形式
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-10-10 DOI: 10.1007/s12188-018-0197-6
Martin Woitalla
{"title":"Modular forms for the (A_{1})-tower","authors":"Martin Woitalla","doi":"10.1007/s12188-018-0197-6","DOIUrl":"10.1007/s12188-018-0197-6","url":null,"abstract":"<div><p>In the 1960s Igusa determined the graded ring of Siegel modular forms of genus two. He used theta series to construct <span>(chi _{5})</span>, the cusp form of lowest weight for the group <span>({text {Sp}}(2,mathbb {Z}))</span>. In 2010 Gritsenko found three towers of orthogonal type modular forms which are connected with certain series of root lattices. In this setting Siegel modular forms can be identified with the orthogonal group of signature (2, 3) for the lattice <span>(A_{1})</span> and Igusa’s form <span>(chi _{5})</span> appears as the roof of this tower. We use this interpretation to construct a framework for this tower which uses three different types of constructions for modular forms. It turns out that our method produces simple coordinates.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 2","pages":"297 - 316"},"PeriodicalIF":0.4,"publicationDate":"2018-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0197-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50018310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A duality theorem for Tate–Shafarevich groups of curves over algebraically closed fields 代数闭域上曲线群的对偶定理
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-10-04 DOI: 10.1007/s12188-018-0196-7
Timo Keller
{"title":"A duality theorem for Tate–Shafarevich groups of curves over algebraically closed fields","authors":"Timo Keller","doi":"10.1007/s12188-018-0196-7","DOIUrl":"10.1007/s12188-018-0196-7","url":null,"abstract":"<div><p>In this note, we prove a duality theorem for the Tate–Shafarevich group of a finite discrete Galois module over the function field <i>K</i> of a curve over an algebraically closed field: there is a perfect duality of finite groups <img> for <i>F</i> a finite étale Galois module on <i>K</i> of order invertible in <i>K</i> and with <span>(F' = {{mathrm{Hom}}}(F,mathbf{Q}/mathbf {Z}(1)))</span>. Furthermore, we prove that <span>(mathrm {H}^1(K,G) = 0)</span> for <i>G</i> a simply connected, quasisplit semisimple group over <i>K</i> not of type <span>(E_8)</span>.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 2","pages":"289 - 295"},"PeriodicalIF":0.4,"publicationDate":"2018-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0196-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50015083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Semisimple weakly symmetric pseudo-Riemannian manifolds 半简单弱对称伪黎曼流形
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-08-29 DOI: 10.1007/s12188-018-0195-8
Zhiqi Chen, Joseph A. Wolf
{"title":"Semisimple weakly symmetric pseudo-Riemannian manifolds","authors":"Zhiqi Chen,&nbsp;Joseph A. Wolf","doi":"10.1007/s12188-018-0195-8","DOIUrl":"10.1007/s12188-018-0195-8","url":null,"abstract":"<div><p>We develop the classification of weakly symmetric pseudo-Riemannian manifolds <i>G</i> / <i>H</i> where <i>G</i> is a semisimple Lie group and <i>H</i> is a reductive subgroup. We derive the classification from the cases where <i>G</i> is compact, and then we discuss the (isotropy) representation of <i>H</i> on the tangent space of <i>G</i> / <i>H</i> and the signature of the invariant pseudo-Riemannian metric. As a consequence we obtain the classification of semisimple weakly symmetric manifolds of Lorentz signature <span>((n-1,1))</span> and trans-Lorentzian signature <span>((n-2,2))</span>.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 2","pages":"331 - 369"},"PeriodicalIF":0.4,"publicationDate":"2018-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0195-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50052486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Non-vanishing of products of Fourier coefficients of modular forms of half-integral weight 半积分权值的模形式的傅里叶系数积的不消失
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-05-16 DOI: 10.1007/s12188-018-0194-9
Winfried Kohnen
{"title":"Non-vanishing of products of Fourier coefficients of modular forms of half-integral weight","authors":"Winfried Kohnen","doi":"10.1007/s12188-018-0194-9","DOIUrl":"10.1007/s12188-018-0194-9","url":null,"abstract":"<div><p>We prove a non-vanishing result in weight aspect for the product of two Fourier coefficients of a Hecke eigenform of half-integral weight.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 2","pages":"371 - 376"},"PeriodicalIF":0.4,"publicationDate":"2018-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0194-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50032824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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