Chebyshev-Like Theorems and the PNT

By Alexander Walker

September 25, 2013

Abstract

Chebyshev's 1852 paper "Memoir sur les nombres premiers" represented the first real progress towards the Prime Number Theorem (PNT) in over a century, proving that $\pi(x)\log x / x$ remains bounded as $x$ tends to infinity. In this talk we give a generalization of Chebyshev's technique, and ask (as Erdos did) whether or not the "Chebyshev method" is strong enough to prove the PNT.