Spectral theory on 3-dimensional hyperbolic space and Hermitian modular forms

被引：2
|
作者：
Matthes, Roland [1 ]
Mizuno, Yoshinori [2 ]
机构：
[1] Univ Kassel, Kassel, Germany
[2] Univ Tokushima, Fac & Sch Engn, Tokushima 7708506, Japan
来源：
FORUM MATHEMATICUM | 2014年 / 26卷 / 06期
关键词：
3-dimensional hyperbolic space; Hermitian modular forms; EISENSTEIN SERIES; FOURIER COEFFICIENTS; EXPLICIT FORMULA; POINCARE-SERIES;
D O I：
10.1515/forum-2011-0113
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study some arithmetics of Hermitian modular forms of degree two by applying the spectral theory on 3-dimensional hyperbolic space. This paper presents three main results: (1) a 3-dimensional analogue of Katok-Sarnak's correspondence, (2) an analytic proof of a Hermitian analogue of the Saito-Kurokawa lift by means of a converse theorem, (3) an explicit formula for the Fourier coefficients of a certain Hermitian Eisenstein series.
引用
收藏
页码：1763 / 1806
页数：44
相关论文
共 50 条
  • [1] ZETA-FUNCTIONS OF BINARY HERMITIAN-FORMS AND SPECIAL VALUES OF EISENSTEIN SERIES ON 3-DIMENSIONAL HYPERBOLIC SPACE
    ELSTRODT, J
    GRUNEWALD, F
    MENNICKE, J
    MATHEMATISCHE ANNALEN, 1987, 277 (04) : 655 - 708
  • [2] ON FOURIER COEFFICIENTS OF MAASS CUSP FORMS IN 3-DIMENSIONAL HYPERBOLIC SPACE
    RAGHAVAN, S
    SENGUPTA, J
    PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 1994, 104 (01): : 77 - 92
  • [3] SPECTRAL THEORY ON THE 3-DIMENSIONAL HYPERBOLIC SPACE AND CLASS-NUMBERS OF BIQUADRATIC NUMBER-FIELDS
    HETRODT, G
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1994, 319 (09): : 921 - 926
  • [4] Digraphs On 3-Dimensional Hyperbolic Space
    Besenk, Murat
    1ST INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES (ICMRS 2018), 2018, 1991
  • [5] DISCONTINUOUS GROUPS ON 3-DIMENSIONAL HYPERBOLIC SPACE - ANALYTICAL THEORY AND ARITHMETIC APPLICATIONS
    ELSTRODT, J
    GRUNEWALD, F
    MENNICKE, J
    RUSSIAN MATHEMATICAL SURVEYS, 1983, 38 (01) : 137 - 168
  • [6] MANNHEIM CURVES IN 3-DIMENSIONAL SPACE FORMS
    Choi, Jin Ho
    Kang, Tae Ho
    Kim, Young Ho
    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2013, 50 (04) : 1099 - 1108
  • [7] On biconservative surfaces in 3-dimensional space forms
    Fetcu, Dorel
    Nistor, Simona
    Oniciuc, Cezar
    COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2016, 24 (05) : 1027 - 1045
  • [8] Bertrand curves in 3-dimensional space forms
    Choi, Jin Ho
    Kang, Tae Ho
    Kim, Young Ho
    APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (03) : 1040 - 1046
  • [9] PRIME GEODESIC THEOREM IN THE 3-DIMENSIONAL HYPERBOLIC SPACE
    Balkanova, Olga
    Chatzakos, Dimitrios
    Cherubini, Giacomo
    Frolenkov, Dmitry
    Laaksonen, Niko
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 372 (08) : 5355 - 5374
  • [10] LATTICE-POINT PROBLEMS IN 3-DIMENSIONAL HYPERBOLIC SPACE
    FRICKER, F
    COMMENTARII MATHEMATICI HELVETICI, 1968, 43 (04) : 402 - &
12345