On the zeros of \(\zeta^{(l)}(s) - a\) (On the zeros of a class of a generalized Dirichlet series. XVII)
type: Item
instance of: scholarly article
title: On the zeros of \(\zeta^{(l)}(s) - a\) (On the zeros of a class of a generalized Dirichlet series. XVII)
zbMATH Open document ID: 0858.11046
DOI: 10.1007/BF02837193
author: K. Ramachandra
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1996-11-10T00:00:00Z
review text: This paper proves very precise results on the roots of \(\zeta^{(l)} (s) = a\) in the region \(\sigma>1\). Here \(a\) is any fixed complex number and \(\zeta^{(l)} (s)\) is the \(l\)-th derivative, where \(l\) is large in terms of \(a\). These results are derived from analogous statements for generalized Dirichlet series, which are themselves proved via Rouché's Theorem.
reviewed by: D. R. Heath-Brown
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 11M41
zbMATH DE Number: 903361
zbMATH Keywords: zeros of generalized Dirichlet series
zbMATH Keywords: Riemann zeta-function
zbMATH Keywords: derivatives
zbMATH Keywords: \(a\)-values
MaRDI profile type: Publication
cites work: On the zeros of ζ'(s)-a
full work available at URL: https://doi.org/10.1007/bf02837193
OpenAlex ID: W2089319411
description: scientific article; zbMATH DE number 903361