On the Critical Strip of the Riemann zeta Fractional Derivative

C. Cattani*, E. Guariglia, S. Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)459-472
Number of pages14
JournalFundamenta Informaticae
Volume151
Issue number1-4
DOIs
Publication statusPublished - 2017
Externally publishedYes

Keywords

  • Critical strip
  • Dirichlet η Functions
  • Fourier transform
  • Fractional derivatives
  • Riemann ζ Functions
  • Signal processings

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