Analytic prime number theory in the twenty-first century, Terence Tao,
8/7/2023, Warsaw - Numbers in the Universe school and conference.
Lecture 1. Small gaps between primes.
We survey the sieve-theoretic methods of Goldston-Pintz-Yildirim, Zhang, Maynard, and the ”Polymath” project that have led to Zhang’s celebrated result that bounded gaps between primes occur infinitely often. We also discuss the ”parity problem” that prevents us from using these methods to resolve the twin prime conjecture.
Course notes:
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