Vol. 301, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Uniform bounds of the Piltz divisor problem over number fields

Wataru Takeda

Vol. 301 (2019), No. 2, 601–616
DOI: 10.2140/pjm.2019.301.601

We consider the upper bound of the Piltz divisor problem over number fields. The Piltz divisor problem is known as a generalization of the Dirichlet divisor problem. We deal with this problem over number fields and improve the error term of this function for many cases. Our proof uses the estimate of exponential sums. We also show uniform results for the ideal counting function and relatively r-prime lattice points as one of its applications.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

ideal counting function, exponential sum, Piltz divisor problem
Mathematical Subject Classification 2010
Primary: 11N45
Secondary: 11R42, 11H06, 11P21
Received: 23 July 2018
Revised: 29 August 2018
Accepted: 31 December 2018
Published: 24 October 2019
Wataru Takeda
Department of Mathematics
Nagoya University