Local zeta functions for a class of p-adic symmetric spaces (II)
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912278808363008 |
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| author | Harinck, Pascale Rubenthaler, Hubert |
| author_facet | Harinck, Pascale Rubenthaler, Hubert |
| contents | In this paper we study the zeta functions associated to the minimal spherical principal series of representations for a class of reductive p-adic symmetric spaces, which are realized as open orbits of some prehomogeneous spaces. These symmetric spaces have been studied in the paper arXiv: 2003.05764. We prove that the zeta functions satisfy a functional equation which is given explicitly (see Theorem 4.3.9 and Theorem 4.4.5). Moreover, for a subclass of these spaces, we define L-functions and epsilon-factors associated to the representations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_06667 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local zeta functions for a class of p-adic symmetric spaces (II) Harinck, Pascale Rubenthaler, Hubert Representation Theory 22E46, 16S32 In this paper we study the zeta functions associated to the minimal spherical principal series of representations for a class of reductive p-adic symmetric spaces, which are realized as open orbits of some prehomogeneous spaces. These symmetric spaces have been studied in the paper arXiv: 2003.05764. We prove that the zeta functions satisfy a functional equation which is given explicitly (see Theorem 4.3.9 and Theorem 4.4.5). Moreover, for a subclass of these spaces, we define L-functions and epsilon-factors associated to the representations. |
| title | Local zeta functions for a class of p-adic symmetric spaces (II) |
| topic | Representation Theory 22E46, 16S32 |
| url | https://arxiv.org/abs/2407.06667 |