Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.09519 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916361334161408 |
|---|---|
| author | Pollack, Aaron |
| author_facet | Pollack, Aaron |
| contents | We prove that the space of cuspidal quaternionic modular forms on the groups of type $F_4$ and $E_n$ have a purely algebraic characterization. This characterization involves Fourier coefficients and Fourier-Jacobi expansions of the cuspidal modular forms. The main component of the proof of the algebraic characterization is to show that certain infinite sums, which are potentially the Fourier expansion of a cuspidal modular form, converge absolutely. As a consequence of the algebraic characterization, we deduce that the cuspidal quaternionic modular forms have a basis consisting of forms all of whose Fourier coefficients are algebraic numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09519 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automatic convergence and arithmeticity of modular forms on exceptional groups Pollack, Aaron Number Theory We prove that the space of cuspidal quaternionic modular forms on the groups of type $F_4$ and $E_n$ have a purely algebraic characterization. This characterization involves Fourier coefficients and Fourier-Jacobi expansions of the cuspidal modular forms. The main component of the proof of the algebraic characterization is to show that certain infinite sums, which are potentially the Fourier expansion of a cuspidal modular form, converge absolutely. As a consequence of the algebraic characterization, we deduce that the cuspidal quaternionic modular forms have a basis consisting of forms all of whose Fourier coefficients are algebraic numbers. |
| title | Automatic convergence and arithmeticity of modular forms on exceptional groups |
| topic | Number Theory |
| url | https://arxiv.org/abs/2408.09519 |