Analytic Number Theory

This group gathers theorems that use the tools of calculus and complex analysis, rather than pure algebra, to prove facts about whole numbers, especially about how primes and other arithmetic quantities behave on average or in the limit. It includes results on primes in arithmetic progressions, sieve methods bounding how densely special sets of integers can occur, estimates for exponential sums, and probabilistic statements, such as the Erdos-Kac theorem, about the typical number of prime factors an integer carries.