Kasana, H. S.; Prasad, G. Maximum term and its rank of an entire Dirichlet series. (English) Zbl 0666.30018 An. Științ. Univ. Al. I. Cuza Iași, N. Ser., Secț. Ia 34, No. 2, 111-116 (1988). Let \(f(s)=\sum^{\infty}_{n=1}a_ n \exp (s\lambda_ n)\) where \(s=\sigma +it\), \(0\leq \lambda_ 1<\lambda_ n<\lambda_{n+1}\to \infty\) as \(n\to \infty\) and \(\lim_{n\to \infty}\log n/\lambda_ n=D<\infty,\) be an entire Dirichlet series of (p,q)-order \(\rho\). Let \(u(\sigma)=\max_{n\geq 1}\{| a_ n| e^{\sigma \lambda_ n}\}\) and \(\nu (\sigma)=\max \{n|\) \(u(\sigma)=| a_ n| e^{\sigma \lambda_ n}\}\) denote the maximum term and rank of f(s). The authors obtain some relations involving the maximum terms of f(s) and its derivatives. They also construct a proximate order, in terms of u(\(\sigma)\), for entire Dirichlet series of (p,q)-order \(\rho\). Reviewer: O.P.Juneja MSC: 30D15 Special classes of entire functions of one complex variable and growth estimates 30B50 Dirichlet series, exponential series and other series in one complex variable Keywords:Dirichlet series PDFBibTeX XMLCite \textit{H. S. Kasana} and \textit{G. Prasad}, An. Științ. Univ. Al. I. Cuza Iași, N. Ser., Secț. Ia 34, No. 2, 111--116 (1988; Zbl 0666.30018)