An Audio Analysis of Elliptic Curves

An elliptic curve is an equation that can be expressed in the form y^2=x^3+ax+b, where a,b are certain rational constants. They can be expressed mod primes p, and the solutions to these curves in this form can be used to define a specific Fourier series (particular sums of periodic sine and cosine functions). These series can then be audialized using techniques such as additive synthesis in order to hear how they behave. The goal of this thesis is to use additive synthesis to analyze elliptic curve data.