Distribution and divisibility of the Fourier coefficients of certain Hauptmoduln

DOI10.1016/j.jnt.2023.01.014OpenAlexW4324102222MaRDI QIDQ2696069

Chiranjit Ray

Publication date: 6 April 2023

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

Full work available at URL: https://arxiv.org/abs/2303.09411

zbMATH Keywords

distributionmodular formscontinued fractioneta-quotientsq-seriesRogers-RamanujanHauptmoduln

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Congruences for modular and (p)-adic modular forms (11F33) Fourier coefficients of automorphic forms (11F30) Dedekind eta function, Dedekind sums (11F20)

Uses Software

• Mathematica

Cites Work

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• Analogues of Ramanujan's partition identities
• A mod \(\ell\) Atkin-Lehner theorem and applications
• The Fourier coefficients of the McKay-Thompson series and the traces of CM values
• Several \(q\)-series related to Ramanujan's theta functions
• New Ramanujan-like congruences modulo powers of 2 and 3 for overpartitions
• Congruences for the Coefficients of Modular Forms and For the Coefficients of j(τ)
• Note on the Parity of the Partition Functions.
• Parity of the coefficients of Klein’s $j$-function
• 2-ADIC PROPERTIES OF CERTAIN MODULAR FORMS AND THEIR APPLICATIONS TO ARITHMETIC FUNCTIONS
• On the parity of the Fourier coefficients of the Hauptmoduln $j_{N}(z)$ and $j_{N}^{+}(z)$
• Multiplicative 𝜂-quotients
• Divisibility Properties of the Fourier Coefficients of the Modular Invariant j(τ)
• Further Congruence Properties of the Fourier Coefficients of the Modular Invariant j(τ)
• Properties of the Coefficients of the Modular Invariant J(τ)

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