CLASS NUMBER FORMULAS FOR CERTAIN BICYCLIC BIQUADRATIC NUMBER FIELDS AS FINITE SUMS INVOLVING JACOBI ELLIPTIC FUNCTIONS

被引：0

作者：

Gomez-Molleda, M. A. ^{[1
]}

Lario, Joan-C. ^{[2
]}

机构：

[1] Univ Malaga, Dept Algebra Geometria & Topol, E-29071 Malaga, Spain

[2] Univ Politecn Cataluna, Dept Matemat Aplicada 2, Barcelona, Spain

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2012年 / 8卷 / 05期

关键词：

Class number formula; Jacobi elliptic functions; Class Field Theory; bicyclic biquadratic number fields;

D O I：

10.1142/S179304211250073X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give formulas for the class numbers of bicyclic biquadratic number fields containing an imaginary quadratic field of class number one. The class number is expressed as a finite sum in terms of the basic Jacobi elliptic functions, playing a similar role as the trigonometric sine in Dirichlet classical class number formula.

引用

页码：1257 / 1270

页数：14

共 15 条

[1] Abramowitz M., 1972, Handbook on Mathematical Functions with Formulas, Graphs, and Mathematical Tables
[2] [Anonymous], 1829, Fundamenta nova theoriae functionum ellipticarum
[3] HASSE CLASS NUMBER PRODUCT FORMULA FOR GENERALIZED DIRICHLET FIELDS AND OTHER TYPES OF NUMBER-FIELDS
BERGER, RI
[J]. MANUSCRIPTA MATHEMATICA, 1992, 76 (3-4) : 397 - 406
[4] Dirichlet P. G. L., 1842, J REINE ANGEW MATH, V24, P291, DOI DOI 10.1515/CRLL.1842.24.291
[5] Durege H, 1861, THEORIE ELLIPTISCHEN
[6] Deconstruction of a Dirichlet-Nazimow formula
Gomez-Molleda, Mariangeles
Lario, Joan-C.
[J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2011, 105 (01) : 109 - 117
[7] Hasse Helmut., 1952, KLASSENZAHL ABELSCHE
[8] Iwaniec H., 2004, AM MATH SOC C PUBLIC, V53
[9] Kubota T., 1953, NAGOYA MATH J, V6, P119
[10] Narkiewicz W, 2004, SpringerMonographsinMathe-matics

← 1 2 →