Jonathan Rogawski

Periods of Eisenstein series: The Galois case

Let G = ResE/F H, where H is a connected reductive group over a number field F and E/F is a quadratic extension. We define the regularized period of an automorphic form of G relative to H, and we express the regularized period of cuspidal Eisenstein series in terms of intertwining periods, which are relative analogues of the standard intertwining operators. This leads to an analogue of the Maass-Selberg relations. The regularized periods appear in the contribution of the continuous spectrum to the relative trace formula.

Endoscopy, theta-liftings, and period integrals for the unitary group in three variables

L-packets for the quasi-split unitary group in three variables U(3). We shall give an explicit parametrization of these L-packets using theta liftings and describe some relations between the structure of L-packets and certain period integrals. We also prove that an endoscopic L-packet contains a unique generic representation in local and global cases. Suppose that G is a reductive algebraic group over a local or global field

Generic representations for the unitary group in three variables

We show that for the quasi-split unitary group in three variables every tempered packet of cuspidal automorphic representations contains a globally generic representation.

The Distributions in the Invariant Trace Formula Are Supported on Characters

J. Arthur put the trace formula in invariant form for all connected reductive groups and certain disconnected ones. However his work was written so as to apply to the general disconnected case, modulo two missing ingredients. This paper supplies one of those missing ingredients, namely an argument in Galois cohomology of a kind first used by D. Kazhdan in the connected case.

On twists of cuspidal representations of GL(2)

Abstract Let be σ Galois automorphism of a number field E. We determine the cuspidal representations π of GL2 ( ) such that σ(π) ⋍ π ⊗ ω for some Hecke character ω. Our result is applied to extend the descent criterion of the base change theorem for GL(2) from cyclic extensions of prime degree to arbitrary cyclic extensions.

On periods of CUSP forms and algebraic cycles forU(3)

In this paper we discuss relations between the following types of conditions on a representationπ in a cuspidalL-packet ofU(3): (1)L(s, π×ξ) has a pole ats=1 for someξ; (2) aperiod ofπ over some algebraic cycle inU(3) (coming from a unitary group in two variables) is non-zero; and (3) π is atheta-series lifting from some unitary group in two variables. As an application of our analysis, we show that the algebraic cycles on theU(3) Shimura variety arenot spanned (over the Hecke algebra) by the modular and Shimura curves coming from unitary subgroups.

Cohomology of Congruence Subgroups of SU (2, 1) p and Hodge Cycles on Some Special Complex Hyperbolic Surfaces

Let G be a semisimple algebraic group over a number field F and set G ∞ = ∏ v∈S ∞ Gv, where S∞ is the set of archimedean places of F. As is well-known, the cohomology of a cocompact lattice Γ ⊂ G ∞ is expressed in terms of the decomposition

Errata to “Average Values of Modular L-series Via the Relative Trace Formula”

{L^2}\left( {\Gamma \backslash {G_\infty }} \right) \simeq \hat \oplus m(\pi ,\Gamma )\pi