Comparison results for certain periods of cusp forms on GL_2n over a totally real number field

Abstract

This article grew out of my talk in 'The Legacy of Srinivasa Ramanujan' conference where I spoke about some techniques to prove algebraicity results for the special values of symmetric cube L-functions attached to the Ramanujan ∆-function. If one wishes to compare these different techniques, then one needs to compare various automorphic periods attached to the symmetric cube transfer of ∆. Motivated by this problem, in this article we provide comparison results for Whittaker-Betti periods, Shalika-Betti periods and relative periods at- tached to a given cohomological cuspidal automorphic representation of GL_2n over a totally real number field.