Harmonic Maass form eigencurves
Abstract
We construct two families of harmonic Maass Hecke eigenforms. This construction answers a question of Mazur about the existence of an "eigencurve-type" object in the world of harmonic Maass forms. Using these families, we construct $p$-adic harmonic Maass forms in the sense of Serre.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2017
- DOI:
- 10.48550/arXiv.1703.09633
- arXiv:
- arXiv:1703.09633
- Bibcode:
- 2017arXiv170309633W
- Keywords:
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- Mathematics - Number Theory;
- 11F03
- E-Print:
- The fourth version has been accepted in Research in the Mathematical Sciences