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Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

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The local invariant for scale structures on mapping spaces 映射空间上尺度结构的局部不变量
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-11-04 DOI: 10.1007/s12188-019-00211-w
Jungsoo Kang
{"title":"The local invariant for scale structures on mapping spaces","authors":"Jungsoo Kang","doi":"10.1007/s12188-019-00211-w","DOIUrl":"10.1007/s12188-019-00211-w","url":null,"abstract":"<div><p>A scale Hilbert space is a natural generalization of a Hilbert space which considers not only a single Hilbert space but a nested sequence of subspaces. Scale structures were introduced by H. Hofer, K. Wysocki, and E. Zehnder as a new concept of smooth structures in infinite dimensions. In this paper, we prove that scale structures on mapping spaces are completely determined by the dimension of domain manifolds. We also give a complete description of the local invariant introduced by U. Frauenfelder for these spaces. Product mapping spaces and relative mapping spaces are also studied. Our approach is based on the spectral resolution of Laplace type operators together with the eigenvalue growth estimate.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00211-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50008809","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
Correction to: On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups 修正:关于同余子群的二阶Siegel模形式的傅里叶系数
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-10-09 DOI: 10.1007/s12188-019-00210-x
Masataka Chida, Hidenori Katsurada, Kohji Matsumoto
{"title":"Correction to: On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups","authors":"Masataka Chida,&nbsp;Hidenori Katsurada,&nbsp;Kohji Matsumoto","doi":"10.1007/s12188-019-00210-x","DOIUrl":"10.1007/s12188-019-00210-x","url":null,"abstract":"","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00210-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50016816","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
Twisted component sums of vector-valued modular forms 向量值模形式的扭分量和
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-10-09 DOI: 10.1007/s12188-019-00209-4
Markus Schwagenscheidt, Brandon Williams
{"title":"Twisted component sums of vector-valued modular forms","authors":"Markus Schwagenscheidt,&nbsp;Brandon Williams","doi":"10.1007/s12188-019-00209-4","DOIUrl":"10.1007/s12188-019-00209-4","url":null,"abstract":"<div><p>We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the underlying finite quadratic module <i>A</i> has order <i>p</i> or 2<i>p</i>, where <i>p</i> is an odd prime. The isomorphisms are given by twisted sums of the components of vector-valued modular forms. Our results generalize work of Bruinier and Bundschuh to the case that the components <span>(F_{gamma })</span> of the vector-valued modular form are antisymmetric in the sense that <span>(F_{gamma } = -F_{-gamma })</span> for all <span>(gamma in A)</span>. As an application, we compute restrictions of Doi–Naganuma lifts of odd weight to components of Hirzebruch–Zagier curves.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00209-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50017157","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: 3
Consequences of functional equations for pairs of p-adic L-functions p进l函数对泛函方程的结果
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-10-05 DOI: 10.1007/s12188-019-00208-5
Cédric Dion, Florian Sprung
{"title":"Consequences of functional equations for pairs of p-adic L-functions","authors":"Cédric Dion,&nbsp;Florian Sprung","doi":"10.1007/s12188-019-00208-5","DOIUrl":"10.1007/s12188-019-00208-5","url":null,"abstract":"<div><p>We prove consequences of functional equations of <i>p</i>-adic <i>L</i>-functions for elliptic curves at supersingular primes <i>p</i>. The results include a relationship between the leading and sub-leading terms (for which we use ideas of Wuthrich and Bianchi), a parity result of orders of vanishing, and invariance of Iwasaswa invariants under conjugate twists of the <i>p</i>-adic <i>L</i>-functions.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00208-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50010205","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
Non-vanishing of Miyawaki type lifts 宫崎式升降机不会消失
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-09-10 DOI: 10.1007/s12188-019-00207-6
Henry H. Kim, Takuya Yamauchi
{"title":"Non-vanishing of Miyawaki type lifts","authors":"Henry H. Kim,&nbsp;Takuya Yamauchi","doi":"10.1007/s12188-019-00207-6","DOIUrl":"10.1007/s12188-019-00207-6","url":null,"abstract":"<div><p>In this paper, we study the non-vanishing of the Miyawaki type lift in various situations. In the case of <i>GSpin</i>(2, 10) constructed in Kim and Yamauchi (Math Z 288(1–2):415–437, 2018), we use the fact that the Fourier coefficient at the identity is closely related to the Rankin–Selberg <i>L</i>-function of two elliptic cusp forms. In the case of the original Miyawaki lifts of Siegel cusp forms, we use the fact that certain Fourier coefficients are the Petersson inner product which is non-trivial. This provides infinitely many examples of non-zero Miyawaki lifts. We give explicit examples of degree 24 and weight 24. We also prove a similar result for Miyawaki lifts for unitary groups. Especially, we obtain an unconditional result on non-vanishing of Miyawaki lifts for <span>(U(n+1,n+1))</span> for each <span>(nequiv 3)</span> mod 4. In the last section, we prove the non-vanishing of the Miyawaki lifts for infinitely many half-integral weight Siegel cusp forms. We give explicit examples of degree 16 and weight <span>(frac{29}{2})</span>.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00207-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50018648","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: 3
A ring of symmetric Hermitian modular forms of degree 2 with integral Fourier coefficients 一个二阶对称厄密模形式的环，具有积分傅立叶系数
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-09-03 DOI: 10.1007/s12188-019-00205-8
Toshiyuki Kikuta
{"title":"A ring of symmetric Hermitian modular forms of degree 2 with integral Fourier coefficients","authors":"Toshiyuki Kikuta","doi":"10.1007/s12188-019-00205-8","DOIUrl":"10.1007/s12188-019-00205-8","url":null,"abstract":"<div><p>We determine the structure over <span>(mathbb {Z})</span> of a ring of symmetric Hermitian modular forms of degree 2 with integral Fourier coefficients whose weights are multiples of 4 when the base field is the Gaussian number field <span>(mathbb {Q}(sqrt{-1}))</span>. Namely, we give a set of generators consisting of 24 modular forms. As an application of our structure theorem, we give the Sturm bounds for such Hermitian modular forms of weight <i>k</i> with <span>(4mid k)</span>, for <span>(p=2)</span>, 3. We remark that the bounds for <span>(pge 5)</span> are already known.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00205-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50007337","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
Analytic properties of twisted real-analytic Hermitian Klingen type Eisenstein series and applications 扭曲实解析hermite Klingen型Eisenstein级数的解析性质及其应用
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-08-19 DOI: 10.1007/s12188-019-00206-7
Soumya Das, Abhash Kumar Jha
{"title":"Analytic properties of twisted real-analytic Hermitian Klingen type Eisenstein series and applications","authors":"Soumya Das,&nbsp;Abhash Kumar Jha","doi":"10.1007/s12188-019-00206-7","DOIUrl":"10.1007/s12188-019-00206-7","url":null,"abstract":"<div><p>We prove the meromorphic continuation and the functional equation of a twisted real-analytic Hermitain Eisenstein series of Klingen type, and as a consequence, deduce similar properties for the twisted Dirichlet series associated to a pair of Hermitian modular forms involving their Fourier–Jacobi coefficients. As an application of our result, we prove that infinitely many of the Fourier–Jacobi coefficients of a non-zero Hermitian cusp form do not vanish in any non-trivial arithmetic progression.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00206-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50036468","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
Willmore surfaces in spheres: the DPW approach via the conformal Gauss map 球体中的Willmore曲面:通过共形高斯映射的DPW方法
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-07-09 DOI: 10.1007/s12188-019-00204-9
Josef F. Dorfmeister, Peng Wang
{"title":"Willmore surfaces in spheres: the DPW approach via the conformal Gauss map","authors":"Josef F. Dorfmeister,&nbsp;Peng Wang","doi":"10.1007/s12188-019-00204-9","DOIUrl":"10.1007/s12188-019-00204-9","url":null,"abstract":"<div><p>The paper builds a DPW approach of Willmore surfaces via conformal Gauss maps. As applications, we provide descriptions of minimal surfaces in <span>({mathbb {R}}^{n+2})</span>, isotropic surfaces in <span>(S^4)</span> and homogeneous Willmore tori via the loop group method. A new example of a Willmore two-sphere in <span>(S^6)</span> without dual surfaces is also presented.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00204-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50016624","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: 6
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":null,"pages":null},"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":null,"pages":null},"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
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