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We study how Rankin-Selberg periods interact with integral structures in spherical Whittaker type representations. Using this representation-theoretic framework, we show that the local Euler factors appearing in the construction of the motivic Rankin-Selberg Euler system for a product of modular forms are integrally optimal; i. e. any construction of this type with any choice of integral input data would give local factors appearing in tame norm relations at p which are integrally divisible by the Euler factor Pₚ^' (Frobₚ^-1) modulo p-1.
Alexandros Groutides (Mon,) studied this question.