On the vanishing order of Jacobi forms at infinity
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909653039841280 |
|---|---|
| author | Li, Jialin Wang, Haowu |
| author_facet | Li, Jialin Wang, Haowu |
| contents | In this paper, we establish two types of upper bounds on the vanishing order of Jacobi forms at infinity. The first type is for classical Jacobi forms, which is optimal in a certain sense. The second type is for Jacobi forms of lattice index. Based on this bound, we obtain a lower bound on the slope of orthogonal modular forms, and we prove that the module of symmetric formal Fourier--Jacobi series on $\mathrm{O}(m,2)$ has finite rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the vanishing order of Jacobi forms at infinity Li, Jialin Wang, Haowu Number Theory 11F46, 11F50, 11F55 In this paper, we establish two types of upper bounds on the vanishing order of Jacobi forms at infinity. The first type is for classical Jacobi forms, which is optimal in a certain sense. The second type is for Jacobi forms of lattice index. Based on this bound, we obtain a lower bound on the slope of orthogonal modular forms, and we prove that the module of symmetric formal Fourier--Jacobi series on $\mathrm{O}(m,2)$ has finite rank. |
| title | On the vanishing order of Jacobi forms at infinity |
| topic | Number Theory 11F46, 11F50, 11F55 |
| url | https://arxiv.org/abs/2506.16083 |