Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
Author index
To appear
Other MSP journals
This article is available for purchase or by subscription. See below.
The number of representations of $n$ as a growing number of squares

John Holley-Reid and Jeremy Rouse

Vol. 16 (2023), No. 5, 727–735

Let rk(n) denote the number of representations of the integer n as a sum of k squares. We give an asymptotic for rk(n) when n grows linearly with k. As a special case, we find that

rn(n) B An n ,

with B 0.2821 and A 4.133.

PDF Access Denied

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
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

sums of squares, circle method, saddle-point method
Mathematical Subject Classification 2010
Primary: 11E25
Secondary: 41A60
Received: 8 October 2019
Revised: 11 May 2022
Accepted: 9 November 2022
Published: 9 December 2023

Communicated by Filip Saidak
John Holley-Reid
Department of Mathematics
Wake Forest University
Winston-Salem, NC
United States
Jeremy Rouse
Department of Mathematics
Wake Forest University
Winston-Salem, NC
United States