##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Jeanine van Order

#### EPFL, Lausanne

## Galois averages of Rankin-Selberg ${\bf L}$-functions

##### Abstract:

\indent I will first review the notion of Galois averages of Rankin-Selberg $L$-functions, in particular those of Rankin-Selberg $L$-functions of weight-two cusp forms times theta series associated to Hecke characters of imaginary quadratic fields. I will then present a conjecture about the behaviour of these averages with the conductor of the character, of which the nonvanishing theorems of Rohrlich, Vatsal and Cornut-Vatsal are special cases. Finally, I will explain a strategy of proof, at least in the setting where the class number is equal to one.

Host: Kiran Kedlaya

### November 10, 2011

### 1:00 PM

### AP&M 7321

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