Ramanujan-type systems of nonlinear ODEs for $\Gamma_0(2)$ and $\Gamma_0(3)$

DOI10.1016/J.EXMATH.2022.04.001arXiv2111.01844WikidataQ113874244 ScholiaQ113874244MaRDI QIDQ6382002

Younes Nikdelan

Publication date: 2 November 2021

Abstract: This paper aims to introduce two systems of nonlinear ordinary differential equations whose solution components generate the graded algebra of quasi-modular forms on Hecke congruence subgroups $Gamm{a}_0(2)$ and $Gamm{a}_0(3)$. Using these systems, we provide the generated graded algebras with an $mathfrak{sl}_2(mathbbC)$-module structure. As applications, we introduce Ramanujan-type tau functions for $Gamm{a}_0(2)$ and $Gamm{a}_0(3)$, and obtain some interesting and non-trivial recurrence and congruence relations.

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Congruences for modular and (p)-adic modular forms (11F33) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11) Moduli, classification: analytic theory; relations with modular forms (14J15) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25)

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