Polyharmonic Maass forms for \(\mathrm{PSL}(2,\mathbb Z)\)

DOI10.1007/s11139-015-9729-1zbMath1418.11077arXiv1508.02652OpenAlexW2254928343MaRDI QIDQ2520573

Robert C. Rhoades, Jeffrey C. Lagarias

Publication date: 16 December 2016

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.02652

zbMATH Keywords

modular formsMaass formsharmonicpolyharmonic

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Other groups and their modular and automorphic forms (several variables) (11F55) Automorphic forms, one variable (11F12)

Related Items

Integral representations of rank two false theta functions and their modularity properties ⋮ AN EXTENSION OF ROHRLICH’S THEOREM TO THE -FUNCTION ⋮ Polyharmonic weak Maass forms of higher depth for \(\mathrm{SL}_2(\mathbb{Z})\) ⋮ Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers ⋮ Traces of CM values and cycle integrals of polyharmonic Maass forms ⋮ Kronecker's first limit formula, revisited ⋮ Modular knots, automorphic forms, and the Rademacher symbols for triangle groups

Uses Software

• DLMF

Cites Work

• Eisenstein series for \(\mathrm{SL}(2)\)
• Cycle integrals of the \(j\)-function and mock modular forms
• Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues
• A generalization of gamma functions and Kronecker's limit formulas
• On two geometric theta lifts
• Mock period functions, sesquiharmonic Maass forms, and non-critical values of \(L\)-functions
• The Gross-Kohnen-Zagier theorem in higher dimensions
• Harmonic Maass forms of weight 1
• Harmonic lifts of modular forms
• Real Bargmann spaces, Fischer decompositions, and sets of uniqueness for polyharmonic functions
• Regularized inner products of modular functions
• Lectures on modular functions of one complex variable
• Die Differentialgleichungen in der Theorie der elliptischen Modulfunktionen. (The differential equations in the theory of elliptic modular functions)
• Real Quadratic Analogs of Traces of Singular Moduli
• p -adic coupling of mock modular forms and shadows
• Shifted polyharmonic Maass forms for ${\rm PSL} (2,{\mathbb Z})$
• Lifting cusp forms to Maass forms with an application to partitions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Polyharmonic Maass forms for \(\mathrm{PSL}(2,\mathbb Z)\)