In this lecture series I will explore several problems of analytic number theory in the context of function fields over a finite field. Some of the problems can be approached by methods different that those of traditional analytic number theory and the resulting theorems can be used to check existing conjectures over the integers, and to generate new ones. Among the problems discussed are: counting primes in short intervals and in arithmetic progressions; Chowla's conjecture on the autocorrelation of the Möbius function, the additive divisor problem, moments of L-functions, and statistics of zeros of L-functions and connections with random matrix theory.
Seminar
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