Summary: Zentralblatt MATH
c 2011 FIZ Karlsruhe
Root numbers of Asai L-functions.
Int. Math. Res. Not. 2008, Article ID rnn125, 25 p. (2008).
Let E/F be a quadratic extension of p-adic fields. The main result of this paper is a computation of
2 , , r, ) for a square integrable representation of GL(n, E) whose Galois conjugate is its dual, where
r is the twisted tensor representation of the dual group introduced by the reviewer [Bull. Soc. Math. Fr.
116, No. 3, 295313 (1988; Zbl 0674.10026)]. This is a twisted version of a computation of C. J. Bushnell
and G. Henniart [Bull. Lond. Math. Soc. 31, No. 5, 534542 (1999; Zbl 0928.22016)]. The proof uses a
result on the corresponding global root number, proved by a method of E. Lapid and S. Rallis [Ann. Math.
(2) 157, No. 3, 891917 (2003; Zbl 1067.11026)], and the discovery by the reviewer [J. Reine Angew. Math.
418, 139172 (1991; Zbl 0725.11026)], that representations of a group G distinguished by a subgroup H
consisting of fixed points of an involution are functorial lifts from another group, in particular in the case
G = GL(n, E) and H = GL(n, F) considered in this paper. Yuval Z. Flicker (Columbus)
Keywords: Asai representations; epsilon factors; distinguished representations