THE ATKIN ORTHOGONAL POLYNOMIALS FOR THE LOW-LEVEL FRICKE GROUPS AND THEIR APPLICATION

DOI10.1142/S1793042111004460zbMath1230.11048OpenAlexW2082382587MaRDI QIDQ3173464

Yuichi Sakai

Publication date: 10 October 2011

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042111004460

zbMATH Keywords

Fricke groupquasimodular formsthe Atkin orthogonal polynomial

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Holomorphic modular forms of integral weight (11F11) Hecke-Petersson operators, differential operators (one variable) (11F25)

Related Items (8)

Supersingular conjectures for the Fricke group ⋮ Supersingular elliptic curves and moonshine ⋮ The Atkin orthogonal polynomials for the Fricke groups of levels 5 and 7 ⋮ The Hasse invariant of the Tate normal form \(E_7\) and the supersingular polynomial for the Fricke group \(\Gamma_0^*(7)\) ⋮ On modular solutions of fractional weights for the Kaneko-Zagier equation for \(\varGamma^*_0(2)\) and \(\varGamma^*_0(3)\) ⋮ On the Hasse invariants of the Tate normal forms \(E_5\) and \(E_7\) ⋮ The Hasse invariant of the Tate normal form \(E_5\) and the class number of \(\mathbb{Q}(\sqrt{-5l})\) ⋮ The number of linear factors of supersingular polynomials and sporadic simple groups

Cites Work

• Arithmetic triangle groups
• On modular forms arising from a differential equation of hypergeometric type
• ON EXTREMAL QUASIMODULAR FORMS

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