The Library
Additive problems with almost prime squares
Tools
Tools
Tools
Blomer, Valentin, Grimmelt, Lasse, Li, Junxian and Rydin Myerson, Simon L. (2023) Additive problems with almost prime squares. Geometric and Functional Analysis, 33 . pp. 1173-1242. doi:10.1007/s00039-023-00635-w ISSN 1016-443X.
|
PDF
s00039-023-00635-w.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (979Kb) | Preview |
|
![[img]](https://wrap.warwick.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
WRAP-Additive-problems-almost-prime-squares-23.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (829Kb) |
Official URL: https://doi.org/10.1007/s00039-023-00635-w
Abstract
We show that every sufficiently large integer is a sum of a prime and two almost prime squares, and also a sum of a smooth number and two almost prime squares. The number of such representations is of the expected order of magnitude. We likewise treat representations of shifted primes p-1 as sums of two almost prime squares. The methods involve a combination of analytic, automorphic and algebraic arguments to handle representations by restricted binary quadratic forms with a high degree of uniformity.
| Item Type: | Journal Article | |||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | |||||||||||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Number theory, Sieves (Mathematics), Forms, Binary, Numbers, Prime, Forms, Quadratic | |||||||||||||||||||||||||||
| Journal or Publication Title: | Geometric and Functional Analysis | |||||||||||||||||||||||||||
| Publisher: | Birkhaeuser Verlag AG | |||||||||||||||||||||||||||
| ISSN: | 1016-443X | |||||||||||||||||||||||||||
| Official Date: | October 2023 | |||||||||||||||||||||||||||
| Dates: |
|
|||||||||||||||||||||||||||
| Volume: | 33 | |||||||||||||||||||||||||||
| Page Range: | pp. 1173-1242 | |||||||||||||||||||||||||||
| DOI: | 10.1007/s00039-023-00635-w | |||||||||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||||||||
| Reuse Statement (publisher, data, author rights): | This version of the article has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/[insert DOI]. Use of this Accepted Version is subject to the publisher’s Accepted Manuscript terms of use https://www.springernature.com/gp/open-research/policies/acceptedmanuscript-terms. | |||||||||||||||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||||||||||||||
| Date of first compliant deposit: | 6 June 2023 | |||||||||||||||||||||||||||
| Date of first compliant Open Access: | 27 July 2023 | |||||||||||||||||||||||||||
| RIOXX Funder/Project Grant: |
|
|||||||||||||||||||||||||||
| Related URLs: | ||||||||||||||||||||||||||||
| Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
