Kloosterman identities over a quadratic extension
This paper proves the fundamental lemma of the relative trace formula for quadratic base change from \(\text{GL} (m,F)\) to \(\text{GL} (m,E)\), where \(E/F\) is a quadratic extension of global fields. The lemma was formulated by \textit{H. Jacquet} and \textit{Y. Ye} [Bull. Soc. Math. Fr. 120, No. 3, 263--295 (1992; Zbl 0785.11032)]. It requires, at almost all places, a matching of certain orbital integrals: a Kloosterman integral on one side with a relative Kloosterman integral on the other side. Jacquet and Ye proved the lemma for \(\text{GL} (3)\) (loc.cit.). The proof for \(\text{GL} (m)\) over local fields of positive characteristic is due to \textit{Ngô Báo Châu} [Duke Math. J. 96, No. 3, 473--520 (1999; Zbl 1047.11517)]. The paper under review proves the conjecture for unramified quadratic extensions of non-Archimedean local fields with the residual characteristic \(\neq 2\).
scientific article; zbMATH DE number 2157790