Analytic Number Theory

Analytic number theory uses the machinery of complex analysis — entire functions, contour integrals, exponential sums — to extract quantitative information about the integers, with the distribution of primes as its central obsession. You'll work through Davenport: deriving the explicit formula and the prime number theorem, extending it to arithmetic progressions via Dirichlet L-functions and Siegel's theorem, then moving into additive problems through the circle method and sieve techniques culminating in Bombieri's theorem. Expect weekly problem sets and a LaTeX presentation on an advanced topic; the course assumes you're comfortable with complex analysis and prepares you for research in multiplicative number theory, sieve methods, or automorphic forms.