Hecke Operators for Maass Waveforms on PSL(2,Z) with Integer Weight and Eta Multiplier

2006/11/06 by Fredrik Strömberg, Strömberg, Fredrik
Mathematics · #11F03 #11F11 (Secondary) #11F25 (Primary) #FOS: Mathematics #Number Theory (math.NT) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0611148

openalex publication_date 2006/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct Hecke operators acting on Maass waveforms of integer non-zero weight and transforming according to a non-trivial multiplier system on the modular group. Using these Hecke operators we obtain multiplicativity relations for the Fourier coefficients of such Maass waveforms. These relations generalize the usual weight zero relations. We also obtain an unexpected relation between coefficients with positive and negative indices with a constant of proportionality involving the Laplace eigenvalue. Numerical examples of multiplicativity relations are given at the end of the paper.

Related

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• Multiplicativity of Fourier Coefficients of Maass Forms for SL(n,\mathbb Z)
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