Shifted polyharmonic Maass forms for ${\rm PSL} (2,{\mathbb Z})$

DOI10.4064/aa170905-7-3zbMath1440.11078arXiv1708.01278OpenAlexW3105658335MaRDI QIDQ4963273

Nickolas Andersen, Robert C. Rhoades, Jeffrey C. Lagarias

Publication date: 1 November 2018

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.01278

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 (6)

A hyperbolic analogue of the Rademacher symbol ⋮ Petersson norms of Eisenstein series and Kohnen-Zagier's formula ⋮ Polyharmonic Maass forms for \(\mathrm{PSL}(2,\mathbb Z)\) ⋮ 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

Uses Software

• DLMF

Cites Work

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• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues
• 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)
• Spectra of hyperbolic surfaces

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