Special Values of L-functions for GL(n) Over a CM Field

Abstract

We prove a Galois-equivariant algebraicity result for the ratios of successive critical values of L-functions for GL(n)/F, where F is a totally imaginary quadratic extension of a totally real number field F+. The proof uses (1) results of Arthur and Clozel on automorphic induction from GL(n)/F to GL(2n)/F+, (2) results of my work with Harder on ratios of critical values for L-functions of GL(2n)/F+, and (3) period relations amongst various automorphic and cohomological periods for GL(2n)/F+ using my work with Shahidi. The reciprocity law inherent in the algebraicity result is exactly as predicted by Deligne's conjecture on the special values of motivic L-functions.