MATH407

This course is aimed at math majors who want a theoretical number theory course beyond MATH 406. Topics will be chosen from finite fields, proof of quadratic reciprocity, Chevalley-Warning theorem on solutions to equations over finite fields, p-adic numbers, Hensel's lemma, Gaussian integers and quadratic fields, the theorem on sums of two squares and four squares, Hilbert symbol, quadratic forms over p-adic fields, Gauss's theorem on sum of three squares, Dirichlet L-functions and Dirichlet's theorem on primes in arithmetic progressions, modular forms, the transcendence of e, theta functions.