Skip Navigation

International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn064, 23 pages, doi:10.1093/imrn/rnn064 published on June 17, 2008
This Article
Right arrow Full Text (PDF)
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Ki, H.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

The Zeros of the Derivative of the Riemann Zeta Function Near the Critical Line

Haseo Ki

Department of Mathematics, Yonsei University, Seoul 120-749, Korea

Correspondence: Correspondence to be sent to: haseo{at}yonsei.ac.kr

We study the horizontal distribution of zeros of {zeta}'(s) which are denoted as {rho}' =β' +i{gamma}'. We assume the Riemann hypothesis which implies β' ≥ 1/2 for any nonreal zero {rho}', equality being possible only at a multiple zero of {zeta} (s). In this paper, we prove that lim inf (β' –1/2)log {gamma}' != 0 if, and only if, for any c > 0 and s = {sigma} + it with 0 ≤|{sigma} -1/2| ≤c/log t (t>t0(c)), we have


Formula 1

where Formula is the zero of {zeta} closest to s (and to the origin, if there are two such). We also show that if lim inf (β'-1/2)log {gamma}' != 0, then for any c>0 and s={sigma} + it (t>t1(c)), we have


Formula 2

uniformly for 1/2+c/log t≤ {sigma} ≤ {sigma} 1 <1.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.