Harmonic symmetry of the Riemann zeta fractional derivative

Abstract

The harmonic properties concerning the fractional derivative of Riemann zeta function are presented through the computation of the double one-sided Fourier transform. In this paper, it is computed both analytically and numerically. The symmetry of this integral transform is shown and discussed through the investigation of real and imagine parts. In addition, the link between the fractional derivative of Riemann zeta function and wavelet analysis is introduced.