Whittaker-Shintani functions for general linear groups over \(p\)-adic fields
As announced in his joint work with \textit{D. Jiang} and \textit{L. Zhang} [Geom. Funct. Anal. 24, No. 2, 552--609 (2014; Zbl 1298.11046); \textit{L. Zhang}, Manuscr. Math. 148, No. 1--2, 213--233 (2015; Zbl 1327.22022)] on calculating local zeta integrals, the author gives an explicit formula for the Whittaker-Shintani function (associated to a pair of unramified characters) for a general linear group over a p-adic field. He also provides a relation between Whittaker-Shintani functions and local Bessel models. As the author indicates, his result is largely based on the work of Kato-Murase-Sugano for orthogonal groups [\textit{S.-i. Kato} et al., Tohoku Math. J. (2) 55, No. 1, 1--64 (2003; Zbl 1037.22034)]. There are also analogous results for symplectic groups, by \textit{A. Murase} and \textit{T. Sugano} [Compos. Math. 79, No. 3, 321--349 (1991; Zbl 0731.11026)] and \textit{X. Shen} [Int. Math. Res. Not. 2014, No. 21, 5769--5831 (2014; Zbl 1306.22009)].
scientific article; zbMATH DE number 6850824
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