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2011 Arithmetic theta lifting and $L$-derivatives for unitary groups, I
Yifeng Liu
Algebra Number Theory 5(7): 849-921 (2011). DOI: 10.2140/ant.2011.5.849


We study cuspidal automorphic representations of unitary groups of 2n variables with ϵ-factor 1 and their central L-derivatives by constructing their arithmetic theta liftings, which are Chow cycles of codimension n on Shimura varieties of dimension 2n1 of certain unitary groups. We give a precise conjecture for the arithmetic inner product formula, originated by Kudla, which relates the height pairing of these arithmetic theta liftings and the central L-derivatives of certain automorphic representations. We also prove an identity relating the archimedean local height pairing and derivatives of archimedean Whittaker functions of certain Eisenstein series, which we call an arithmetic local Siegel–Weil formula for archimedean places. This provides some evidence toward the conjectural arithmetic inner product formula.


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Yifeng Liu. "Arithmetic theta lifting and $L$-derivatives for unitary groups, I." Algebra Number Theory 5 (7) 849 - 921, 2011.


Received: 2 April 2010; Revised: 20 October 2010; Accepted: 21 October 2010; Published: 2011
First available in Project Euclid: 20 December 2017

zbMATH: 1258.11060
MathSciNet: MR2928563
Digital Object Identifier: 10.2140/ant.2011.5.849

Primary: 11G18
Secondary: 11F27, 11G50, 20G05

Rights: Copyright © 2011 Mathematical Sciences Publishers


Vol.5 • No. 7 • 2011
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