Differentiability of the Riemann Function via Fejér-Lanczos Factors

Abstract

The Fourier series can be differentiated employing the Fejér-Lanczos factors; here this approach is applied to the Riemann function to verify with numerical experimentation the Gerver’s result, namely, that its derivative exists and is equal to -1/2 at any point πξ, where ξ is a rational number whose numerator and denominator are odd.