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On the critical strip of the Riemann zeta fractional derivative. (English) Zbl 1376.26007

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.

MSC:

26A33 Fractional derivatives and integrals
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
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