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.
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