# COHOMOLOGICAL AUTOMORPHIC FORMS ON UNITARY GROUPS, II: PERIOD RELATIONS AND VALUES OF L-FUNCTIONS

@inproceedings{Harris2007COHOMOLOGICALAF,
title={COHOMOLOGICAL AUTOMORPHIC FORMS ON UNITARY GROUPS, II: PERIOD RELATIONS AND VALUES OF L-FUNCTIONS},
author={Michael Harris},
year={2007}
}
• M. Harris
• Published 1 November 2007
• Mathematics
This is the fourth in a series of articles devoted to the study of special values of L-functions of automorphic forms contributing to the cohomology of Shimura varieties attached to unitary groups, for the most part those attached to hermitian vector spaces over an imaginary quadratic field K. Since these L-functions are all supposed to be motivic, all their values at integer points are conjectured to be arithmetically meaningful. For the finite set of integer points which are critical in the…
Deligne's conjecture for automorphic motives over CM-fields, Part I: factorization
• Mathematics
• 2018
This is the first of two papers devoted to the relations between Deligne's conjecture on critical values of motivic $L$-functions and the multiplicative relations between periods of arithmetically
Automorphic Galois representations and the cohomology of Shimura varieties
The first part of this report describes the class of representations of Galois groups of number fields that have been attached to automorphic representations. The construction is based on the program
Period relations for automorphic forms on unitary groups and critical values of $L$-functions
In this paper we explore some properties of periods attached to automorphic representations of unitary groups over CM fields and the critical values of their $L$-functions. We prove a formula
L-FUNCTIONS AND PERIODS OF ADJOINT MOTIVES
The article studies the compatibility of the refined Gross-Prasad (or IchinoIkeda) conjecture for unitary groups, due to Neal Harris, with Deligne’s conjecture on critical values of L-functions. When
Chow groups and $L$-derivatives of automorphic motives for unitary groups
• Mathematics
Annals of Mathematics
• 2021
In this article, we study the Chow group of the motive associated to a tempered global $L$-packet $\pi$ of unitary groups of even rank with respect to a CM extension, whose global root number is
Arithmetic theta lifts and the arithmetic Gan–Gross–Prasad conjecture for unitary groups
• Hang Xue
• Mathematics
Duke Mathematical Journal
• 2019
In 1980s, Gross–Zagier [GZ86] established a formula that relates the Neron–Tate height of Heegner points on modular curves to the central derivative of certain L-functions associated to modular
A Refined Gross-Prasad Conjecture for Unitary Groups
Let F be a number field, AF its ring of adeles, and let [pi]n and [pi]n+1 be irreducible, cuspidal, automorphic representations of SOn(AF) and SOn+1AF), respectively. In 1991, Benedict Gross and
Unitary Eigenvarieties at Isobaric Points
Abstract In this article we study the geometry of the eigenvarieties of unitary groups at points corresponding to tempered non-stable representations with an anti-ordinary (a.k.a evil) refinement. We

## References

SHOWING 1-10 OF 25 REFERENCES
Theta dichotomy for unitary groups
• Mathematics
• 1996
Some recent work of Gross and Prasad [14] suggests that the root numbers attached to certain symplectic representations of the Weil-Deligne group of a local field F control certain branching rules
Howe Correspondence for Real Unitary Groups
Roger Howe proved that for any reductive dual pair (G, G′) in the symplectic groupSp(2n, R), there is a one-to-one correspondence of irreducible admissible representations of some two-fold covers
Correspondances de Howe sur un corps p-adique
• Mathematics
• 1987
This book grew out of seminar held at the University of Paris 7 during the academic year 1985-86. The aim of the seminar was to give an exposition of the theory of the Metaplectic Representation (or
Automorphic forms with degenerate Fourier coefficients
The main theme of this paper is that singular automorphic forms on classical groups are given by theta series liftings. We establish several inequalities relating the automorphic multiplicities of a
On First Occurrence in the Local Theta Correspondence
• Mathematics
• 2004
This paper discusses a conservation conjecture for the first occurrence indices. Such indices record the first occurrence of an irreducible admissible representation π of a fixed group G in the local
Conditional Base Change for Unitary Groups
• Mathematics
• 2004
It has been known for many years that the stabilization of the Arthur-Selberg trace formula would, or perhaps we should write “will,” have important consequences for the Langlands functoriality
Arithmeticity in the theory of automorphic forms
Introduction Automorphic forms and families of abelian varieties Arithmeticity of automorphic forms Arithmetic of differential operators and nearly holomorphic functions Eisenstein series of simpler
Degenerate principal series and local theta correspondence
• Mathematics
• 1998
Following our previous paper [LZ] which deals with the groupU(n, n), we study the structure of certain Howe quotients Ω p,q and Ω p,q (1) which are natural Sp(2n,R) modules arising from the
A regularized Siegel-Weil formula for unitary groups
Abstract.For the quasi-split unitary group U(n,n), we prove a refined analogue of the result of S. S. Kudla and S. Rallis on an identity (a regularized Siegel-Weil formula) between a residue of an
Arithmetic vector bundles and automorphic forms on Shimura varieties. I
© Foundation Compositio Mathematica, 1986, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions