##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Lillian Pierce

#### Oxford University

## Quadratic forms, primes, and the circle method

##### Abstract:

Over the last hundred years, the circle method has become one of the most important tools of analytic number theory. This talk (on joint work with Roger Heath-Brown) will describe a new application of the circle method to pairs of quadratic forms, via a novel two-dimensional analogue of Kloosterman's version of the circle method. As a result, we prove (under a mild geometric constraint) that any two quadratic forms with integer coefficients, in 5 variables or more, simultaneously attain prime values infinitely often.

Host: Kiran Kedlaya

### November 20, 2012

### 9:00 AM

### AP&M 6402

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