Arithmetic theta lifting and L-derivatives for unitary groups, II

Yifeng Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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)Q of square-free level.

Original languageEnglish (US)
Pages (from-to)923-1000
Number of pages78
JournalAlgebra and Number Theory
Issue number6
StatePublished - 2011


  • Arithmetic inner product formula
  • Arithmetic theta lifting
  • L-derivatives
  • Unitary Shimura curves

ASJC Scopus subject areas

  • Algebra and Number Theory


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