Đề tài " Kloosterman identities over a quadratic extension "

We prove an identity of Kloosterman integrals which is the fundamental lemma of a relative trace formula for the general linear group in n variables. 1. Introduction One of the simplest examples of Langlands’ principle of functoriality is the quadratic base change. Namely, let E/F be a quadratic extension of global fields and z
→ z the corresponding Galois conjugation. The base change associates to every automorphic representation π of GL(n, F) an automorphic representation Π of GL(n,E). If n = 1 then π is an id`ele class character and Π(z) = π(zz)....