Arithmetic properties for the minus space of weakly holomorphic modular forms

DOI10.1016/j.jnt.2018.09.006zbMath1439.11110OpenAlexW2897714295MaRDI QIDQ1627950

Kyung Seung Lee, So Young Choi, Chang Heon Kim

Publication date: 3 December 2018

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2018.09.006

zbMATH Keywords

Fricke groupduality relationsAtkin-Lehner involutionweakly holomorphic modular formFricke involutionintegrality of the Fourier coefficientsminus spaceminus space of weakly holomorphic modular forms

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Holomorphic modular forms of integral weight (11F11)

Related Items (7)

Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms ⋮ Hecke equivariance of generalized Borcherds products of type \(O(2,1)\) ⋮ Congruences for Hecke eigenvalues in minus spaces ⋮ Bounds for the coefficients of cusp forms for \(\Gamma_{0}(3)\) ⋮ A family of weakly holomorphic modular forms for $\Gamma _0(2)$ with all zeros on a certain geodesic ⋮ Ramanujan-style congruences for prime level ⋮ Dimension formulas for modular form spaces with character for Fricke groups

Cites Work

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• \(p\)-adic properties of coefficients of basis for the space of weakly holomorphic modular forms of weight 2
• Congruences for coefficients of modular functions
• Modular forms on the Fricke group
• Basis for the space of weakly holomorphic modular forms in higher level cases
• Kronecker’s Limit Formula, Holomorphic Modular Functions, andq-Expansions on Certain Arithmetic Groups
• Certain aspects of holomorphic function theory on some genus-zero arithmetic groups
• The Values of Modular Functions and Modular Forms
• Divisibility properties of coefficients of level $p$ modular functions for genus zero primes
• p-Adic Properties of Coefficients of Weakly Holomorphic Modular Forms
• Congruence Subgroups Associated to the Monster
• 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)
• Ramanujan Identities Involving the Partition Function for the Moduli 11 a
• Modular Forms

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