A critical case of Rallis inner product formula

作者：Wu ChenYan^*

来源：Science China Mathematics, 2017, 60(2): 201-222.

DOI：10.1007/s11425-015-0770-7

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

Let pi 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 p 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.

• 出版日期2017-2
• 单位复旦大学