Kronecker’s Limit Formula, Holomorphic Modular Functions, andq-Expansions on Certain Arithmetic Groups

DOI10.1080/10586458.2015.1053161zbMath1417.11041arXiv1309.0648OpenAlexW1526788457MaRDI QIDQ2815499

Holger Then, Lejla Smajlovic, Jay A. Jorgenson

Publication date: 29 June 2016

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.0648

zbMATH Keywords

Eisenstein seriesHauptmodulKronecker limit formula$q$-expansions

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Relationship to Lie algebras and finite simple groups (11F22) Structure of modular groups and generalizations; arithmetic groups (11F06) Holomorphic modular forms of integral weight (11F11)

Related Items (15)

Arithmetic properties for the minus space of weakly holomorphic modular forms ⋮ Effective bounds for Fourier coefficients of certain weakly holomorphic modular forms ⋮ A note on non-ordinary primes for some genus-zero arithmetic groups ⋮ Modular Dedekind symbols associated to Fuchsian groups and higher-order Eisenstein series ⋮ KRONECKER LIMIT FUNCTIONS AND AN EXTENSION OF THE ROHRLICH–JENSEN FORMULA ⋮ Applications of Kronecker's limit formula for elliptic Eisenstein series ⋮ Weight 1/2 multiplier systems for the group \(\Gamma_0^+ (p)\) and a geometric formulation ⋮ Certain aspects of holomorphic function theory on some genus-zero arithmetic groups ⋮ Transformation laws for generalized Dedekind sums associated to Fuchsian groups ⋮ Kronecker limit formulas for parabolic, hyperbolic and elliptic Eisenstein series via Borcherds products ⋮ On the Evaluation of Singular Invariants for Canonical Generators of Certain Genus One Arithmetic Groups ⋮ The Hauptmodul at elliptic points of certain arithmetic groups ⋮ Some results in study of Kronecker limit formula and Dedekind sums ⋮ An explicit evaluation of the Hauptmoduli at elliptic points for certain arithmetic groups ⋮ An approach for computing generators of class fields of imaginary quadratic number fields using the Schwarzian derivative

Cites Work

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• Monstrous Moonshine
• Finite Groups and Modular Functions
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• How to Compute the Coefficients of the Elliptic Modular Functionj(z)
• Generalized modular forms representable as eta products
• Congruence Subgroups of Groups Commensurable with PSL (2, Z) of Genus 0 and 1
• Moonshine beyond the Monster
• The Fourier Coefficients of the Modular Invariant J(τ)

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