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MR2448081 (2009h:11083) 11F70 (11F67 22E50)
Anandavardhanan, U. K. (6IIT)
Root numbers of Asai Lfunctions.
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 padic field E and r is the Asai Lfunction.
Recall that, if E/F is a quadratic extension, is a representation of the Lgroup
L
[RE/F GL(n)] = GLn(C) × GLn(C) Gal(E/F),
which is in fact equivalent to the adjoint action of the Lgroup 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
LanglandsShahidi philosophy, that the Asai Lfunction 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 selfdual, then (1
