Cattani, C.; Guariglia, E.; Wang, S. On the critical strip of the Riemann zeta fractional derivative. (English) Zbl 1376.26007 Fundam. Inform. 151, No. 1-4, 459-472 (2017). Summary: The \(\alpha\)-order fractional derivative of the Dirichlet \(\eta\) function is computed in order to investigate the behavior of the fractional derivative of the Riemann zeta function \(\zeta^{(\alpha)}\) on the critical strip. The convergence of \(\eta^{(\alpha)}\) is studied. In particular, its half-plane of convergence gives the possibility to better understand the \(\zeta^{(\alpha)}\) and its critical strip. As an application, two signal processing networks, corresponding to \(\eta^{(\alpha)}\) and to its Fourier transform respectively, are shortly described. Cited in 9 Documents MSC: 26A33 Fractional derivatives and integrals 11M06 \(\zeta (s)\) and \(L(s, \chi)\) Keywords:fractional derivatives; Riemann \(\zeta\) functions; Dirichlet \(\eta\) functions; signal processings; Fourier transform; critical strip PDFBibTeX XMLCite \textit{C. Cattani} et al., Fundam. Inform. 151, No. 1--4, 459--472 (2017; Zbl 1376.26007) Full Text: DOI