##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Ameya Pitale

#### Ohio-State University

## Lifting of cusp forms from \tilde{SL}_2 to GSpin(1,4)

##### Abstract:

We construct liftings of cuspidal automorphic forms from the metaplectic group $\tilde{SL}_2$ to GSpin(1,4) using Maass Converse Theorem. In order to prove the non-vanishing of the lift, we derive Waldspurger's formula for Fourier coefficients of half integer weight Maass forms. We analyze the automorphic representation of the adelic spin group obtained from the lift and show that it is CAP to the Saito-Kurokawa lift from $\tilde{SL}_2$ to GSp_4.

Host: Wee Teck Gan

### April 27, 2006

### 3:00 PM

### AP&M 7321

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