Cycle integrals of meromorphic Hilbert modular forms
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929375568461824 |
|---|---|
| author | Alfes, Claudia Depouilly, Baptiste Kiefer, Paul Schwagenscheidt, Markus |
| author_facet | Alfes, Claudia Depouilly, Baptiste Kiefer, Paul Schwagenscheidt, Markus |
| contents | We establish a rationality result for linear combinations of traces of cycle integrals of certain meromorphic Hilbert modular forms. These are meromorphic counterparts to the Hilbert cusp forms $ω_m(z_1,z_2)$, which Zagier investigated in the context of the Doi-Naganuma lift. We give an explicit formula for these cycle integrals, expressed in terms of the Fourier coefficients of harmonic Maass forms. A key element in our proof is the explicit construction of locally harmonic Hilbert-Maass forms on $\mathbb{H}^2$, which are analogous to the elliptic locally harmonic Maass forms examined by Bringmann, Kane, and Kohnen. Additionally, we introduce a regularized theta lift that maps elliptic harmonic Maass forms to locally harmonic Hilbert-Maass forms and is closely related to the Doi-Naganuma lift. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cycle integrals of meromorphic Hilbert modular forms Alfes, Claudia Depouilly, Baptiste Kiefer, Paul Schwagenscheidt, Markus Number Theory We establish a rationality result for linear combinations of traces of cycle integrals of certain meromorphic Hilbert modular forms. These are meromorphic counterparts to the Hilbert cusp forms $ω_m(z_1,z_2)$, which Zagier investigated in the context of the Doi-Naganuma lift. We give an explicit formula for these cycle integrals, expressed in terms of the Fourier coefficients of harmonic Maass forms. A key element in our proof is the explicit construction of locally harmonic Hilbert-Maass forms on $\mathbb{H}^2$, which are analogous to the elliptic locally harmonic Maass forms examined by Bringmann, Kane, and Kohnen. Additionally, we introduce a regularized theta lift that maps elliptic harmonic Maass forms to locally harmonic Hilbert-Maass forms and is closely related to the Doi-Naganuma lift. |
| title | Cycle integrals of meromorphic Hilbert modular forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2406.03465 |