Geodesic
On Ramanujan's modular equations and Hecke groups
Md. Shafiul Alam1
1 University of Barishal, Department of Mathematics, and Tohoku University, Graduate School of Information Sciences
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 461–471.

Voir la notice de l'article provenant de la source Journal.fi

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.
DOI : 10.54330/afm.146802
Keywords: Modular equation, hypergeometric function, Hecke group, congruence subgroup

Md. Shafiul Alam 1

1 University of Barishal, Department of Mathematics, and Tohoku University, Graduate School of Information Sciences 
@article{AFM_2024_49_2_a2,
     author = {Md. Shafiul Alam},
     title = {On {Ramanujan's} modular equations and {Hecke} groups},
     journal = {Annales Fennici Mathematici},
     pages = {461{\textendash}471--461{\textendash}471},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2024},
     doi = {10.54330/afm.146802},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.54330/afm.146802/}
}
TY  - JOUR
AU  - Md. Shafiul Alam
TI  - On Ramanujan's modular equations and Hecke groups
JO  - Annales Fennici Mathematici
PY  - 2024
SP  - 461–471
EP  - 461–471
VL  - 49
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.54330/afm.146802/
DO  - 10.54330/afm.146802
LA  - en
ID  - AFM_2024_49_2_a2
ER  - 
%0 Journal Article
%A Md. Shafiul Alam
%T On Ramanujan's modular equations and Hecke groups
%J Annales Fennici Mathematici
%D 2024
%P 461–471-461–471
%V 49
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.54330/afm.146802/
%R 10.54330/afm.146802
%G en
%F AFM_2024_49_2_a2
Md. Shafiul Alam. On Ramanujan's modular equations and Hecke groups. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 461–471. doi : 10.54330/afm.146802. http://geodesic.mathdoc.fr/articles/10.54330/afm.146802/

Cité par Sources :