A critical case of Rallis inner product formula

Chenyan Wu

Research output: Contribution to journalArticlepeer-review

Abstract

Let π be a genuine cuspidal representation of the metaplectic group of rank n. We consider the theta lifts to the orthogonal group associated to a quadratic space of dimension 2n+1. We show a case of regularised Rallis inner product formula that relates the pairing of theta lifts to the central value of the Langlands L-function of π twisted by a character. The bulk of this paper focuses on proving a case of regularised Siegel-Weil formula, on which the Rallis inner product formula is based and whose proof is missing in the literature.

Original languageEnglish (US)
Pages (from-to)201-222
Number of pages22
JournalScience China Mathematics
Volume60
Issue number2
DOIs
StatePublished - Feb 1 2017

Keywords

  • L-function
  • Rallis inner product formula
  • regularised Siegel-Weil formula
  • theta lift

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