On the Critical Strip of the Riemann zeta Fractional Derivative

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Cattani, C.^{a; *} | Guariglia, E.^{b; †} | Wang, S.^c

Affiliations: [a] Engineering School (DEIM), University of Tuscia, Largo dell’Università, 01100 Viterbo, Italy. cattani@unitus.it | [b] Dept. of Physics “E. R. Caianiello”, University of Salerno, Via Giovanni Paolo II, 84084 Fisciano, Italy. eguariglia@unisa.it, emanuel.guariglia@mdh.se | [c] School of Electronic Science and Engineering, Nanjing University, Nanjing, Jiangsu 210046, China. wangshuihua@njnu.edu.cn

Correspondence: [*] Address for correspondence: Engineering School (DEIM), University of Tuscia, Largo dell’Università, 01100 Viterbo, Italy

Note: [†] Also affiliated at: Division of Applied Mathematics, Mälardalen University, 721 23 Västerås/Eskilstuna, Sweden

Abstract: The α-order fractional derivative of the Dirichlet η function is computed in order to investigate the behavior of the fractional derivative of the Riemann zeta function ζ(α) on the critical strip. The convergence of η(α) is studied. In particular, its half-plane of convergence gives the possibility to better understand the ζ(α) and its critical strip. As an application, two signal processing networks, corresponding to η(α) and to its Fourier transform respectively, are shortly described.

Keywords: Fractional derivatives, Riemann ζ functions, Dirichlet η functions, signal processings, Fourier transform, critical strip

DOI: 10.3233/FI-2017-1504

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 459-472, 2017