On Ramanujan's modular equations and Hecke groups

被引：0
|
作者：
Alam, Shafiul [1 ,2 ]
机构：
[1] Univ Barishal, Dept Math, Barishal 8254, Bangladesh
[2] Tohoku Univ, Grad Sch Informat Sci, Aoba Ku, Sendai 9808579, Japan
来源：
ANNALES FENNICI MATHEMATICI | 2024年 / 49卷 / 02期
关键词：
Modular equation; hypergeometric function; Hecke group; congruence subgroup;
D O I：
10.54330/afm.146802
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Inspired by the work of Ramanujan, many people have studied generalized modular equations and the numerous identities found by Ramanujan. These identities known as modular equations can be transformed into polynomial equations. There is no developed theory about how to find the degrees of these polynomial modular equations explicitly. In this paper, we determine the degrees of the polynomial modular equations explicitly and study the relation between Hecke groups and modular equations in Ramanujan's theories of signatures 2, 3, and 4.
引用
收藏
页码：461 / 471
页数：11
相关论文
共 50 条
  • [21] Modular Equations for the Rogers-Ramanujan Continued Fraction and the Dedekind Eta-Function
    Jinhee Yi
    The Ramanujan Journal, 2001, 5 : 377 - 384
  • [22] Modular equations for the Rogers-Ramanujan continued fraction and the Dedekind eta-function
    Yi, JH
    RAMANUJAN JOURNAL, 2001, 5 (04) : 377 - 384
  • [23] Growth in Hecke groups
    Kreuzer, Martin
    Rosenberger, Gerhard
    RIEMANN AND KLEIN SURFACES, AUTOMORPHISMS, SYMMETRIES AND MODULI SPACES, 2014, 629 : 261 - 281
  • [24] Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms
    Dixit, Atul
    Roy, Arindam
    Zaharescu, Alexandru
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 426 (01) : 594 - 611
  • [25] Principal congruence subgroups of hecke groups H(√q)
    Özgür, NY
    ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2006, 22 (02) : 383 - 392
  • [26] Some Modular Relation on Analogous of Ramanujan's Remarkable Product of Theta-Function
    Dharmendra, B. N.
    Kumar, M. C. Mahesh
    Nagendra, P.
    BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2022, 40
  • [27] Normal Subgroups of Hecke Groups H(λ)
    Koruoglu, Oezden
    Sahin, Recep
    Ikikardes, Sebahattin
    Cangul, Ismail Naci
    ALGEBRAS AND REPRESENTATION THEORY, 2010, 13 (02) : 219 - 230
  • [28] Power subgroups of some Hecke groups
    Ikikardes, Sebahattin
    Koruoglu, Ozden
    Sahin, Recep
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2006, 36 (02) : 497 - 508
  • [29] On suborbital graphs for some Hecke groups
    Keskin, R
    DISCRETE MATHEMATICS, 2001, 234 (1-3) : 53 - 64
  • [30] Normal Subgroups of Hecke Groups H(λ)
    Özden Koruoğlu
    Recep Sahin
    Sebahattin İkikardes
    Ismail Naci Cangül
    Algebras and Representation Theory, 2010, 13 : 219 - 230
12345