In mathematics, the Odlyzko–Schönhage algorithm is a fast algorithm for evaluating the Riemann zeta function at many points, introduced by (Odlyzko & Schönhage ). The main point is the use of the fast Fourier transform to speed up the evaluation of a finite Dirichlet series of length N at O(N) equally spaced values from O(N2) to O(N1+ε) steps (at the cost of storing O(N1+ε) intermediate values). The Riemann–Siegel formula used for calculating the Riemann zeta function with imaginary part T uses a finite Dirichlet series with about N = T1/2 terms, so when finding about N values of the Riemann zeta function it is sped up by a factor of about T1/2. This reduces the time to find the zeros of the zeta function with imaginary part at most T from about T3/2+ε steps to about T1+ε steps.