Vol. 295, No. 2, 2018

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ISSN: 0030-8730
Theta correspondence and the Prasad conjecture for SL(2)

Hengfei Lu

Vol. 295 (2018), No. 2, 477–498
Abstract

We use relations between the base change representations and theta lifts, to give a new proof to the local period problems of SL(2) over a nonarchimedean quadratic field extension EF. Then we verify the Prasad conjecture for  SL(2). With a similar strategy, we obtain a certain result for the Prasad conjecture for Sp(4).

Keywords
theta lifts, periods, base change, Prasad's conjecture
Mathematical Subject Classification 2010
Primary: 11F27, 11F70, 22E50
Milestones
Received: 12 September 2017
Revised: 6 February 2018
Accepted: 22 February 2018
Published: 11 April 2018
Authors
Hengfei Lu
School of Mathematics
Tata Institute of Fundamental Research
School of Mathematics
Colaba
Mumbai
India