Vinogradov’s Three-Prime Theorem (with Sammy Luo and Ryan Alweiss)

This was my final paper for 18.099, seminar in discrete analysis, jointly with Sammy Luo and Ryan Alweiss. We prove that every sufficiently large odd integer can be written as the sum of three primes, conditioned on a strong form of the prime number theorem. 1. Introduction In this paper, we prove the following result:… Continue reading Vinogradov’s Three-Prime Theorem (with Sammy Luo and Ryan Alweiss)

Things Fourier

For some reason several classes at MIT this year involve Fourier analysis. I was always confused about this as a high schooler, because no one ever gave me the ``orthonormal basis'' explanation, so here goes. As a bonus, I also prove a form of Arrow's Impossibility Theorem using binary Fourier analysis, and then talk about… Continue reading Things Fourier