Twisted traces of CM values of weak Maass forms

2011/08/31 by Claudia Alfes‐Neumann, Claudia Alfes, Stephan Ehlen · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #Lift (data mining) #Mathematical analysis #Mathematics #Moduli #Physics #Pure mathematics #math.NT #msc:11F37

paper · pdf · doi:10.1016/j.jnt.2012.10.008

published as Journal of Number Theory 133 (6), 2013 · Some minor corrections, mostly typos. Added Journal reference

openalex publication_date 2013/01/16 · arxiv created 2013/04/04 · arxiv updated 2013/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that the twisted traces of CM values of weak Maass forms of weight 0 are Fourier coefficients of vector valued weak Maass forms of weight 3/2. These results generalize work by Zagier on traces of singular moduli. We utilize a twisted version of the theta lift considered by Bruinier and Funke.

Citations

• Heegner divisors, L-functions and harmonic weak Maass forms
• Arithmetic properties of coefficients of half-integral weight Maass–Poincaré series
• Heegner points and derivatives ofL-series. II
• Heegner points, cycles and Maass forms
• On two geometric theta lifts
• Heegner points and derivatives ofL-series

Cited by

• A modular framework for generalized Hurwitz class numbers III