On critical values of Rankin-Selberg convolutions

Kasten, H.
Schmidt, C.-G.

facul_08; 10

Abstract:
For a pair $(\pi,\sigma)$ of cuspidal automorphic representations of $\GL_n$ and $\GL_{n-1}$, both of non-vanishing cohomology with possibly non-trivial coefficients, 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 an associated archimedean Rankin-Selberg pairing on the cohomology is established for $n=3$.

Primary MSC: 11F67 Special values of automorphic L­series, periods of modular forms, cohomology, modular symbols
Secondary MSC: 17B10 Representations, algebraic theory (weights), 17B56 Cohomology of Lie (super)algebras, 22E55 Representations of Lie and linear algebraic groups over global fields and ad‘ ele rings
Keywords: special values of automorphic $L$-functions, Lie algebra cohomology