##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## David Krumm

#### Claremont McKenna College

## Squarefree parts of polynomial values

##### Abstract:

Let C be a hyperelliptic curve defined over the rational numbers, and consider the set S of all squarefree integers d such that the quadratic twist of C by d has a rational point. In this talk we will discuss the question of whether, given a prime number p, the set S contains representatives from all congruence classes modulo p. When C has genus 0 this question can be answered using elementary number theory, but for higher genera it seems to require the use of big conjectures in arithmetic geometry.

### March 6, 2014

### 12:00 PM

### AP&M 7321

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