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MR2448081 (2009h:11083) 11F70 (11F67 22E50)
Anandavardhanan, U. K. (6-IIT)
Root numbers of Asai L-functions.
Int. Math. Res. Not. IMRN 2008, Art.ID rnn125, 25 pp.
The main result of this paper is the computation of the epsilon factor (1
2, , r, ), where is
a square integrable representation of GL(n) over a p-adic field E and r is the Asai L-function.
Recall that, if E/F is a quadratic extension, is a representation of the L-group
[RE/F GL(n)] = GLn(C) × GLn(C) Gal(E/F),
which is in fact equivalent to the adjoint action of the L-group on the Lie algebra of the unipotent
radical of a certain parabolic subgroup P of the unitary group U(n, n). It is then clear, from the
Langlands-Shahidi philosophy, that the Asai L-function occurs in the constant term of certain
Eisenstein series on U(n, n).
Theorem 1.2 of the paper states that, if E/F is a quadratic extension of number fields and is
irreducible, cuspidal, and conjugate self-dual, then (1