Rankin–Selberg gamma factors of level zero representations of GL n

Abstract

Abstract For a p-adic local field F of characteristic 0, with residue field 𝔣 {\mathfrak{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 {\mathfrak{f}} . Our results can be used to prove a variant of Jacquet’s conjecture on the local converse theorem.