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- W2535476387 abstract "According to Sakellaridis, many zeta integrals in the theory of automorphic forms can be produced or explained by appropriate choices of a Schwartz space of test functions on a spherical homogeneous space, which are in turn dictated by the geometry of affine spherical embeddings. We pursue this perspective by developing a local counterpart and try to explicate the functional equations. These constructions are also related to the $L^2$-spectral decomposition of spherical homogeneous spaces in view of the Gelfand-Kostyuchenko method. To justify this viewpoint, we prove the convergence of $p$-adic local zeta integrals under certain premises, work out the case of prehomogeneous vector spaces and re-derive a large portion of Godement-Jacquet theory. Furthermore, we explain the doubling method and show that it fits into the paradigm of $L$-monoids developed by L. Lafforgue, B. C. Ngo et al., by reviewing the constructions of Braverman and Kazhdan (2002). In the global setting, we give certain speculations about global zeta integrals, Poisson formulas and their relation to period integrals." @default.
- W2535476387 created "2016-10-28" @default.
- W2535476387 creator A5073063405 @default.
- W2535476387 date "2018-01-01" @default.
- W2535476387 modified "2023-09-27" @default.
- W2535476387 title "Towards Generalized Prehomogeneous Zeta Integrals" @default.
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- W2535476387 doi "https://doi.org/10.1007/978-3-319-95231-4_6" @default.
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