Abstract
The construction of L functions for automorphic cuspidal representations of GSp(4, A) × GL(2, A) with a Whittaker model has been given by Novodvorsky [Novodvorsky, M. (1979) Proc. Symp. Pure Math. 33 (2), 87-95]. In this paper, we prove that this L function has nontrivial poles if and only if the representation of GSp(4, A) is a lifting from split O4. We also introduce a different construction of L functions for GSp(4) × GL(2) that is applicable to representations that do not have a Whittaker model—for instance, those that correspond to holomorphic modular forms. This construction is based on the lifting of these automorphic forms to Sp(4). Lifted forms will have a Whittaker model. This allows us to write integral expressions yielding these L functions.
Keywords: automorphic form, Whittaker model, Weil representation, Eisenstein series
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