Critical values of Rankin-Selberg L-functions for GL(n) x GL(n-1) and the symmetric cube L-functions for GL(2)
arXiv:1312.5955
Abstract
In a previous article we had proved an algebraicity result for the central critical value for L-functions for GL(n) x GL(n-1) over Q assuming the validity of a nonvanishing hypothesis involving archimedean integrals. The purpose of this article is to generalize that result for all critical values for L-functions for GL(n) x GL(n-1) over any number field F. Binyong Sun has recently proved that nonvanishing hypothesis and so the results of this article are unconditional. Using such results for the case of GL(3) x GL(2), new unconditional algebraicity results for the special values of symmetric cube L-functions for GL(2) over F have been proved.
This revised version, now 35 pages, is to appear in Forum Mathematicum. A previous version of this article had an appendix by Chandrasheel Bhagwat, and upon a referee's suggestion this appendix has been deleted from this current version, and will be appearing as a separate note under the sole authorship of Chandrasheel Bhagwat in C.R.Math.Acad.Sci.Paris