##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Wee Teck Gan

#### UCSD

## The Refined Gross-Prasad Conjecture

##### Abstract:

The Gross-Prasad conjecture says that the period integral of a cuspidal representation of SO(n+1) x SO(n) over the diagonal SO(n) is nonzero if and only if the central critical value of a certain L-function does not vanish. There is a refinement of the conjecture, due to Ichino-Ikeda, which gives a formula for the central L-value in terms of the period integral. I will explain this refined conjecture, and discuss some joint work with Ichino in the case n=4. The case n=2 is a classic theorem of Waldspurger and the case n=3 is a recent theorem of Ichino.

### November 6, 2008

### 1:00 PM

### AP&M 7321

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