Translator Disclaimer
2011 Arithmetic theta lifting and $L$-derivatives for unitary groups, II
Yifeng Liu
Algebra Number Theory 5(7): 923-1000 (2011). DOI: 10.2140/ant.2011.5.923

Abstract

We prove the arithmetic inner product formula conjectured in the first paper of this series for n=1, that is, for the group U(1,1)F unconditionally. The formula relates central L-derivatives of weight-2 holomorphic cuspidal automorphic representations of U(1,1)F with ϵ-factor 1 with the Néron–Tate height pairing of special cycles on Shimura curves of unitary groups. In particular, we treat all kinds of ramification in a uniform way. This generalizes the arithmetic inner product formula obtained by Kudla, Rapoport, and Yang, which holds for certain cusp eigenforms of PGL(2) of square-free level.

Citation

Download Citation

Yifeng Liu. "Arithmetic theta lifting and $L$-derivatives for unitary groups, II." Algebra Number Theory 5 (7) 923 - 1000, 2011. https://doi.org/10.2140/ant.2011.5.923

Information

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

zbMATH: 1258.11061
MathSciNet: MR2928564
Digital Object Identifier: 10.2140/ant.2011.5.923

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

Rights: Copyright © 2011 Mathematical Sciences Publishers

JOURNAL ARTICLE
78 PAGES


SHARE
Vol.5 • No. 7 • 2011
MSP
Back to Top