Vol. 295, No. 2, 2018

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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).

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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