Journal article
Additive problems with almost prime squares
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 969.3KB, Terms of use)
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- Publisher copy:
- 10.1007/s00039-023-00635-w
Authors
+ European Research Council
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- Funder identifier:
- https://ror.org/0472cxd90
- Grant:
- 851318
- 648329
- Programme:
- Horizon 2020
+ Deutsche Forschungsgemeinschaft
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- Funder identifier:
- https://ror.org/018mejw64
- Grant:
- EXC-2047/1-390685813
- BL 915/5-1
- BL 915/2-2
- 255083470
- Programme:
- Germany’s Excellence Strategy Grant
+ Leverhulme Trust
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- Funder identifier:
- https://ror.org/012mzw131
- Programme:
- Early Career Fellowship
+ Max Planck Institute for Mathematics
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- Funder identifier:
- https://ror.org/02dh8ja68
- Publisher:
- Springer
- Journal:
- Geometric and Functional Analysis More from this journal
- Volume:
- 33
- Issue:
- 5
- Pages:
- 1173-1242
- Publication date:
- 2023-06-19
- Acceptance date:
- 2023-02-20
- DOI:
- EISSN:
-
1420-8970
- ISSN:
-
1016-443X
- Language:
-
English
- Keywords:
- Pubs id:
-
1489594
- Local pid:
-
pubs:1489594
- Deposit date:
-
2025-07-31
- ARK identifier:
Terms of use
- Copyright holder:
- Blomer et al.
- Copyright date:
- 2023
- Rights statement:
- © 2023 The Authors. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
- Licence:
- CC Attribution (CC BY)
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