Abstract
By comparing two different evaluations of a modified (à la Borcherds) higher Siegel theta lift on even lattices of signature (r,s), we prove Eichler–Selberg relations for a wide class of negative-weight vector-valued mock modular forms. In doing so, we detail several properties of the lift, as well as showing that it produces an infinite family of local (and locally harmonic) Maaß forms on Grassmanians in certain signatures.
| Original language | English |
|---|---|
| Pages (from-to) | 381-406 |
| Number of pages | 26 |
| Journal | Pacific Journal of Mathematics |
| Volume | 322 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 23 May 2023 |
Bibliographical note
Funding Information:The research conducted by Males for this paper is supported by the Pacific Institute for the Mathematical Sciences (PIMS). The research and findings may not reflect those of the institute. Mono was supported by the CRC/TRR 191 “Symplectic Structures in Geometry, Algebra and Dynamics”, funded by the DFG (project number 281071066). MSC2020: primary 11F27; secondary 11F37. Keywords: higher Siegel theta lift, Eichler–Selberg relations, local Maass forms, vector-valued mock modular forms.
Publisher Copyright:
© 2023 MSP (Mathematical Sciences Publishers).
Keywords
- math.NT
- 11F27 (Primary), 11F37 (Secondary)