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In a previous article we had proved an algebraicity result for the centralcritical value for L-functions for GL(n) x GL(n-1) over Q assuming the validityof a nonvanishing hypothesis involving archimedean integrals. The purpose ofthis article is to generalize that result for all critical values forL-functions for GL(n) x GL(n-1) over any number field F. Binyong Sun hasrecently proved that nonvanishing hypothesis and so the results of this articleare unconditional. Using such results for the case of GL(3) x GL(2), newunconditional algebraicity results for the special values of symmetric cubeL-functions for GL(2) over F have been proved.

Critical values of Rankin-Selberg L-functions for GL(n) x GL(n-1) and the symmetric cube L-functions for GL(2)