Rankin-Selberg gamma factors of level zero representations of GLn

For a p-adic local field F of characteristic 0, with residue field f, we prove that the Rankin -Selberg gamma factor of a pair of level zero representations of linear general groups over F is equal to a gamma factor of a pair of corresponding cuspidal representations of linear general groups over f. Our results can be used to prove a variant of Jacquet's conjecture on the local converse theorem.