Counting Points over Finite Fields

Goal:

We look at solutions of polynomial equations f(x,y)=0 over finite fields and try to discover patterns in the number of such solutions. In fact, we are counting points on curves over finite fields. With little experimenting very quickly you will see some patterns arising. Prerequisites are that you know what a finite field is and that you are willing to experiment to find the number of solutions with a computer (or even by hand if you have enough perseverance). Once you see some patterns appear the successive experiments will present themselves. The project file suggests step by step what experiment to do. At the end you know what to do.

Supervisors: Gerard van der Geer, Bryan Advocaat

Difficulty level: Any

Tools: Any programming language or any Computer Algebra System

Bibliography: Upon request

FSTC -- University of Luxembourg