##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Everett W. Howe

#### Center for Communications Research

## Producing genus-4 curves with many points

##### Abstract:

Abstract: I will talk about a computational problem inspired by the desire to improve the tables of curves over finite fields with many points (http://www.manypoints.org). Namely, if $q$ is a large prime power, how does one go about producing a genus-4 curve over $\mathbb F_q$ with many points? I will discuss the background to this problem and give a number of algorithms, one of which one expects (heuristically!) to produce a genus-4 curve whose number of points is quite close to the Weil upper bound in time $O\left(q^{3/4 + \epsilon}\right).$

Host: Alina Bucur

### February 14, 2012

### 1:00 PM

### AP&M 5402

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