A new class of modular equation for Weber functions

被引：2
作者：
Hart, William B. [1 ]
机构：
[1] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2007年 / 3卷 / 01期
基金：
英国工程与自然科学研究理事会;
关键词：
Weber functions; modular equations;
D O I：
10.1142/S1793042107000845
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe the construction of a new type of modular equation for Weber functions. These bear some relationship to Weber's modular equations of the irrational kind. Numerous examples of these equations are explicitly computed. We also obtain some modular equations of the irrational kind which are not present in Weber's work.
引用
收藏
页码：141 / 157
页数：17
相关论文
共 11 条
[1]  
Berndt B. C., 1991, Ramanujan's Notebooks
[2]   Ramanujan's class invariants, Kronecker's limit formula, and modular equations [J].
Berndt, BC ;
Chan, HH ;
Zhang, LC .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (06) :2125-2173
[3]   On Russell-type modular equations [J].
Chan, HH ;
Liaw, WC .
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2000, 52 (01) :31-46
[4]   Congruence subgroups of PSL(2, Z) of genus less than or equal to 24 [J].
Cummins, CJ ;
Pauli, S .
EXPERIMENTAL MATHEMATICS, 2003, 12 (02) :243-255
[5]  
HART W, IN PRESS RAMANUJAN J
[6]  
HART W, CLASS INVARIANTS NEW
[7]  
HART WB, 2004, THESIS MACQUARIE U S
[8]   RAMANUJAN MODULAR EQUATIONS [J].
RAMANATHAN, KG .
ACTA ARITHMETICA, 1990, 53 (04) :403-420
[9]  
Schoeneberg B., 1974, Die Grundlehren der mathematischen Wissenschaften., V203
[10]  
Weber, 1961, LEHRBUCH ALGEBRA
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