A Fourier-Jacobi Dirichlet series for cusp forms on orthogonal groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909797749620736 |
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| author | Psyroukis, Rafail |
| author_facet | Psyroukis, Rafail |
| contents | We investigate a Dirichlet series involving the Fourier-Jacobi coefficients of two cusp forms $F,G$ for orthogonal groups of signature $(2,n+2)$. In the case when $F$ is a Hecke eigenform and $G$ is a Maass lift of a Poincaré series, we establish a connection with the standard $L$-function attached to $F$. What is more, we find explicit choices of orthogonal groups, for which we obtain a clear-cut Euler product expression for this Dirichlet series. Through our considerations, we recover a classical result for Siegel modular forms, first introduced by Kohnen and Skoruppa, but also provide a range of new examples, which can be related to other kinds of modular forms, such as paramodular, Hermitian, and quaternionic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18663 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Fourier-Jacobi Dirichlet series for cusp forms on orthogonal groups Psyroukis, Rafail Number Theory 11F55, 11E88, 11M41 (Primary) 11E81, 11E41 (Secondary) We investigate a Dirichlet series involving the Fourier-Jacobi coefficients of two cusp forms $F,G$ for orthogonal groups of signature $(2,n+2)$. In the case when $F$ is a Hecke eigenform and $G$ is a Maass lift of a Poincaré series, we establish a connection with the standard $L$-function attached to $F$. What is more, we find explicit choices of orthogonal groups, for which we obtain a clear-cut Euler product expression for this Dirichlet series. Through our considerations, we recover a classical result for Siegel modular forms, first introduced by Kohnen and Skoruppa, but also provide a range of new examples, which can be related to other kinds of modular forms, such as paramodular, Hermitian, and quaternionic. |
| title | A Fourier-Jacobi Dirichlet series for cusp forms on orthogonal groups |
| topic | Number Theory 11F55, 11E88, 11M41 (Primary) 11E81, 11E41 (Secondary) |
| url | https://arxiv.org/abs/2407.18663 |