On a relation between sums of arithmetical functions and Dirichlet series
type: Item
instance of: scholarly article
title: On a relation between sums of arithmetical functions and Dirichlet series
zbMATH Open document ID: 1274.11144
DOI: 10.2298/PIM1206097I
author: Hideaki Ishikawa
author: Yuichi Kamiya
publication date: 2013-10-18T00:00:00Z
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 6217230
zbMATH Keywords: analytic continuation
MaRDI profile type: Publication
published in: Publications de l'Institut Mathématique. Nouvelle Série
review text: The authors introduce a concept called good oscillation. A function is called good oscillation, if its \(m\)-tuple integrals are bounded by functions having mild orders. They prove that, if the error terms coming from summatory functions of arithmetical functions are good oscillation, then the Dirichlet series associated with those arithmetical functions can be continued analytically over the whole plane. The authors also study a sort of converse assertion that if the Dirichlet series are continued analytically over the whole plane and satisfy a certain additional assumption, then the error terms coming from the summatory functions of Dirichlet coefficients are good oscillation. As an application they consider the multiple Dirichlet series generated by characters \(\chi_k(n)\) (\(k =1,\dots,j\)) to the same modulus \(q\) (\(\geq 2\)).
reviewed by: Aleksandar Ivić
description: scientific article; zbMATH DE number 6217230