Journal article
Sums of transcendental dilates
- Abstract:
- We show that there is an absolute constant $c > 0$ such that $|A+\lambda \cdot A|\geqslant e^{c\sqrt {\log |A|}}|A|$ for any finite subset $A$ of $\mathbb {R}$ and any transcendental number $\lambda \in \mathbb {R}$. By a construction of Konyagin and Łaba, this is best possible up to the constant $c$.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
-
-
(Preview, Accepted manuscript, pdf, 318.2KB, Terms of use)
-
- Publisher copy:
- 10.1112/blms.12870
Authors
+ Directorate for Mathematical & Physical Sciences
More from this funder
- Funder identifier:
- https://ror.org/029b7h395
- Publisher:
- Wiley
- Journal:
- Bulletin of the London Mathematical Society More from this journal
- Volume:
- 55
- Issue:
- 5
- Pages:
- 2400-2406
- Publication date:
- 2023-06-08
- Acceptance date:
- 2023-04-27
- DOI:
- EISSN:
-
1469-2120
- ISSN:
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0024-6093
- Language:
-
English
- Pubs id:
-
1489925
- Local pid:
-
pubs:1489925
- Deposit date:
-
2025-12-26
- ARK identifier:
Terms of use
- Copyright holder:
- Conlon and Lim
- Copyright date:
- 2023
- Rights statement:
- © 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Wiley at https://dx.doi.org/10.1112/blms.12870
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