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

Yifeng Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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 2n - 1 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.

Original languageEnglish (US)
Pages (from-to)849-921
Number of pages73
JournalAlgebra and Number Theory
Issue number6
StatePublished - 2011


  • Arithmetic inner product formula
  • Arithmetic theta lifting
  • L-derivatives
  • Special cycles

ASJC Scopus subject areas

  • Algebra and Number Theory


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