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 language | English (US) |
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Pages (from-to) | 201-222 |
Number of pages | 22 |
Journal | Science China Mathematics |
Volume | 60 |
Issue number | 2 |
DOIs | |
State | Published - Feb 1 2017 |
Keywords
- L-function
- Rallis inner product formula
- regularised Siegel-Weil formula
- theta lift