In this paper we study the analytic properties of the standard L-function attached to vector valued quaternionic modular forms using the Rankin-Selberg method. This involves the construction of vector valued theta series, which we obtain by applying some differential operators on Jacobi-theta series studied by Krieg. Such differential operators are obtained from the Howe-Weyl duality for the pair Spn(C) × GL2n(C).
Bouganis, A. (2021). On the standard L-function attached to quaternionic modular forms. Journal of Number Theory, 222, 293-345. https://doi.org/10.1016/j.jnt.2020.10.024