Riesz-type criteria for the Riemann hypothesis

Archit Agarwal, Meghali Garg, Bibekananda Maji

In 1916, Riesz proved that the Riemann hypothesis is equivalent to the bound $\sum_{n=1}^\infty \frac{μ(n)}{n^2} \exp\left( - \frac{x}{n^2} \right) = O_ε \left( x^{-\frac{3}{4} + ε…