Frederik Broucke

On the connection between zero-free regions and the error term in the prime number theorem

Abstract We provide for a wide class of zero-free regions an upper bound for the error term in the Prime Number Theorem, refining works of Pintz (1980), Johnston (2024), and Révész (2024). Our method does not only apply to the Riemann zeta function, but to general Beurling zeta f...