Accessibility navigation


Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem

Hilberdink, T. W. (2010) Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem. Journal of Number Theory, 130 (3). pp. 707-715. ISSN 0022-314X

[img] Text - Accepted Version
· Please see our End User Agreement before downloading.

196kB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1016/j.jnt.2009.09.008

Abstract/Summary

In this paper we study generalised prime systems for which the integer counting function NP(x) is asymptotically well behaved, in the sense that NP(x)=ρx+O(xβ), where ρ is a positive constant and . For such systems, the associated zeta function ζP(s) is holomorphic for . We prove that for , for any ε>0, and also for ε=0 for all such σ except possibly one value. The Dirichlet divisor problem for generalised integers concerns the size of the error term in NkP(x)−Ress=1(ζPk(s)xs/s), which is O(xθ) for some θ<1. Letting αk denote the infimum of such θ, we show that .

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:23360
Uncontrolled Keywords:Beurling's generalised primes; Dirichlet divisor problem
Publisher:Elsevier

Downloads

Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation