The Critical Values of Rankin–selberg Convolutions

For a pair (π, σ) of cuspidal automorphic representations of GL n and GL n-1 , both of non-vanishing cohomology, we show algebraicity properties of critical values of the associated Rankin–Selberg L-function twisted by finite-order characters. A certain non-vanishing assumption about the associated archimedean Rankin–Selberg pairings on the cohomology is established for n = 3.