Carletti, E.; Bragadin, G. Monti On analytic continuation and functional equation of certain Dirichlet series. (English) Zbl 0782.30005 Int. J. Math. Math. Sci. 16, No. 3, 609-614 (1993). The well-known functional equation of the Riemann zeta function \(\zeta(s)\) is \[ 2^{1-s} \Gamma(s) \zeta(s)\cos \left( {{s\pi} \over 2} \right)= \pi^ s \zeta(1-s),\tag{1} \] where \(s\) is a complex variable. If we set \(\xi(s)=\pi^{-{s\over 2}} \Gamma({s\over 2}) \zeta(s)\), then (1) can be written as (2) \(\xi(s)=\xi(1-s)\).In this paper the authors investigate analytic continuation and functional equation of Riemann’s type (see the above (1) and (2)) of Dirichlet series by using one of Riemann’s methods [see E. C. Titchmarsh, The theory of the Riemann zeta function (1986; Zbl 0601.10026)]. Reviewer: H.Haruki (Waterloo / Ontario) MSC: 30B50 Dirichlet series, exponential series and other series in one complex variable 30B40 Analytic continuation of functions of one complex variable Keywords:Riemann zeta function; functional equation; Dirichlet series Citations:Zbl 0601.10026 PDFBibTeX XMLCite \textit{E. Carletti} and \textit{G. M. Bragadin}, Int. J. Math. Math. Sci. 16, No. 3, 609--614 (1993; Zbl 0782.30005) Full Text: DOI EuDML