The Riemann hypothesis is true up to $3\cdot 10^{12}$

Abstract

We verify numerically, in a rigorous way using interval arithmetic, that the Riemann hypothesis is true up to height $3\cdot 10^{12}$. That is, all zeroes $\beta +i\gamma$ of the Riemann zeta-function with $0<\gamma \le 3\cdot 10^{12}$ have $\beta =1/2$.

References in corpus (1)

• Jensen Polynomials for the Riemann Xi Function

Cited by in corpus (1)

• Zeros of Jensen polynomials and asymptotics for the Riemann xi function