##### Department of Mathematics,

University of California San Diego

****************************

### Math 256 - Representation Theory

## Kartik Prasanna

#### UCLA

## Periods of modular forms on Shimura curves

##### Abstract:

We study the relation between the Petersson norm of a holomorphic GL(2) form $f$ and that of its (suitably normalized) Jacquet-Langlands lift $g$ to a Shimura curve. The ratio of these two norms was previously shown to be algebraic by Shimura and rational by Harris-Kudla. We prove an integrality result for this ratio and explain the arithmetic significance of this ratio in terms of certain congruences satisfied by $f$

Host: Wee Teck Gan

### November 25, 2003

### 1:30 PM

### AP&M 7321

****************************