##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Jonathan Sands

#### University of Vermont and UCSD

## L-functions for multi-quadratic extensions of number fields at s=-1 and annihilation of the tame kernel

##### Abstract:

Brumer's conjecture uses abelian L-functions at $s=0$ to produce group-ring elements which should annihilate class groups of number fields. We consider the analogous conjecture at $s=-1$, and give evidence in the setting of a number field obtained as the composite of several relative quadratic extensions of the base field.

### November 9, 2006

### 1:00 PM

### AP&M 7321

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