Journal article

### A class of non-holomorphic modular forms III: real analytic cusp forms for $\mathrm{SL}_2(\mathbb{Z})$

Abstract:

We define canonical real analytic versions of modular forms of integral weight for the full modular group, generalising real analytic Eisenstein series. They are harmonic Maass waveforms with poles at the cusp, whose Fourier coefficients involve periods and quasi-periods of cusp forms, which are conjecturally transcendental. In particular, we settle the question of finding explicit ‘weak harmonic lifts’ for every eigenform of integral weight k and level one. We show that mock modular forms of...

Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version

### Access Document

Files:
• (pdf, 734.1KB)
Publisher copy:
10.1007/s40687-018-0151-3

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
All Souls College
Role:
Author
Publisher:
Springer Verlag Publisher's website
Journal:
Research in the Mathematical Sciences Journal website
Volume:
34
Issue:
5
Publication date:
2018-08-13
Acceptance date:
2018-07-20
DOI:
EISSN:
2197-9847
ISSN:
2522-0144
Pubs id:
pubs:889540
URN:
uri:a6bf96fe-4d4e-45d9-a474-584d10f3c077
UUID:
uuid:a6bf96fe-4d4e-45d9-a474-584d10f3c077
Local pid:
pubs:889540