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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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Science China Press

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10.1007/bf00855912

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1869-1862

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A critical case of Rallis inner product formula

Authors: ChenYan Wu
Publish Date: 2016/09/14
Volume: 60, Issue: 2, Pages: 201-222
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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 Lfunction of π twisted by a character The bulk of this paper focuses on proving a case of regularised SiegelWeil formula on which the Rallis inner product formula is based and whose proof is missing in the literatureThe author thanks his adviser Professor ShouWu Zhang for lots of helpful conversations and encouragement during the preparation of the bulk of this paper The author also thanks Professor Dihua Jiang for his patience with the author’s nagging questions on the topic and for pointing out a flaw in the original argument

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