#### 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 $SL\left(2\right)$ over a nonarchimedean quadratic field extension $E∕F$. Then we verify the Prasad conjecture for  $SL\left(2\right)$. With a similar strategy, we obtain a certain result for the Prasad conjecture for $Sp\left(4\right)$.

##### Keywords
theta lifts, periods, base change, Prasad's conjecture
##### Mathematical Subject Classification 2010
Primary: 11F27, 11F70, 22E50