On some arithmetic properties of automorphic forms of GLm over a division algebra

Grobner, Harald ; Raghuram, A. (2014) On some arithmetic properties of automorphic forms of GLm over a division algebra International Journal of Number Theory, 10 (04). pp. 963-1013. ISSN 1793-0421

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Official URL: http://www.worldscientific.com/doi/abs/10.1142/S17...

Related URL: http://dx.doi.org/10.1142/S1793042114500110


In this paper we investigate arithmetic properties of automorphic forms on the group G' = GLm/D, for a central division-algebra D over an arbitrary number field F. The results of this article are generalizations of results in the split case, i.e. D = F, by Shimura, Harder, Waldspurger and Clozel for square-integrable automorphic forms and also by Franke and Franke–Schwermer for general automorphic representations. We also compare our theorems on automorphic forms of the group G′ to statements on automorphic forms of its split form using the global Jacquet–Langlands correspondence developed by Badulescu and Badulescu–Renard. Beside that we prove that the local version of the Jacquet–Langlands transfer at an archimedean place preserves the property of being cohomological.

Item Type:Article
Source:Copyright of this article belongs to World Scientific Publishing Co.
Keywords:Inner Forms Of GLn; Global Jacquet–Langlands; Algebraic Representations; Regular Algebraic Representations; Cuspidal Automorphic Forms; Rationality Properties; A픮(Λ)-Modules; Unitary Dual
ID Code:105997
Deposited On:01 Feb 2018 17:01
Last Modified:01 Feb 2018 17:01

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