Seven-modular lattices and a septic base Jacobi identity

被引：8

作者：

Chan, HH ^{[1
]}

Chua, KS

Solé, P

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

[2] Inst High Performance Comp, Singapore 117528, Singapore

[3] ESSI, CNRS 13S, F-06903 Sophia Antipolis, France

来源：

JOURNAL OF NUMBER THEORY | 2003年 / 99卷 / 02期

关键词：

D O I：

10.1016/S0022-314X(02)00069-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A quadratic Jacobi identity to the septic base is introduced and proved by means of modular lattices and codes over rings. As an application the theta series of all the 6-dimensional 7-modular lattices with an Hermitian structure over Q(root-7) are derived. (C) 2002 Elsevier Science (USA). All rights reserved.

引用

页码：361 / 372

页数：12

共 18 条

[1] Applications of coding theory to the construction of modular lattices [J].

Bachoc, C .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1997, 78 (01) :92-119

[2] RAMANUJANS THEORIES OF ELLIPTIC FUNCTIONS TO ALTERNATIVE BASES [J].

BERNDT, BC ;

BHARGAVA, S ;

GARVAN, FG .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (11) :4163-4244

[3]

BERNDT BC, 2001, COMMUNICATION SEP

[4] A CUBIC COUNTERPART OF JACOBIS IDENTITY AND THE AGM [J].

BORWEIN, JM ;

BORWEIN, PB .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 323 (02) :691-701

[5] On Eisenstein series and Σm,n=-∞∞ qm(2)+mn+2n(2) [J].

Chan, HH ;

Ong, YL .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (06) :1735-1744

[6] The root lattice A*n and Ramanujan's circular summation of theta functions [J].

Chua, KS .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (01) :1-8

[7]

COHEN AM, 1976, ANN SCI ECOLE NORM S, V9, P379

[8]

Conway J. H., 1999, GRUNDLEHREN MATH WIS, V290

[9]

ELKIES ND, 1999, EIGHTFOLD WAY, V35

[10]

Frenkel I., 1988, Pure and Applied Mathematics

← 1 2 →