##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Michael Volpato

#### UCSD

## Integral embeddings of quaternions into octonions

##### Abstract:

We study a Siegel-Weil identity between a theta series and an Eisenstein series of genus three. In particular, this yields a Siegel modular form of genus three whose Fourier coefficients count the number of arithmetic embeddings of definite quaternion orders into the Coxeter order of integral octonions.

### January 29, 2009

### 1:00 PM

### AP&M 7321

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