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THE CRITICAL VALUES OF RANKIN–SELBERG CONVOLUTIONS

HENDRIK KASTEN

Mathematisches Institut, Universität Heidelberg, 69120 Heidelberg, Germany

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and

CLAUS-GÜNTHER SCHMIDT

Institut für Algebra und Geometrie, Karlsruher Institut für Technologie, 76128 Karlsruhe, Germany

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https://doi.org/10.1142/S1793042112501345Cited by:14 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 11F67, 17B10, 17B56, 22E55

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