Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Oliver Roche-Newton"'
Publikováno v:
Israel Journal of Mathematics. 248:39-66
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::78e93a3ee5d28b4c129bc66368838867
https://doi.org/10.1007/s11856-022-2291-9
https://doi.org/10.1007/s11856-022-2291-9
Autor:
Cosmin Pohoata, Oliver Roche-Newton
Publikováno v:
Random Structures & Algorithms. 60:749-770
This paper is mainly concerned with sets which do not contain four-term arithmetic progressions, but are still very rich in three term arithmetic progressions, in the sense that all sufficiently large subsets contain at least one such progression. We
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6d649a1bc92c4d63f15c34005b643bf6
https://doi.org/10.1002/rsa.21042
https://doi.org/10.1002/rsa.21042
Publikováno v:
International Mathematics Research Notices. 2022:1154-1172
We prove a nontrivial energy bound for a finite set of affine transformations over a general field and discuss a number of implications. These include new bounds on growth in the affine group, a quantitative version of a theorem by Elekes about rich
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::677e32ef297aa8e73ce26667ad9264f8
https://doi.org/10.1093/imrn/rnaa130
https://doi.org/10.1093/imrn/rnaa130
Autor:
Audie Warren, Oliver Roche-Newton
Publikováno v:
Discrete & Computational Geometry. 66:552-574
The purpose of this article is to further explore how the structure of the affine group can be used to deduce new incidence theorems, and to explore sum-product type applications of these incidence bounds, building on the recent work of Rudnev and Sh
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7f940df04c0adc78629329ee42892c50
https://doi.org/10.1007/s00454-020-00194-z
https://doi.org/10.1007/s00454-020-00194-z
Autor:
Oliver Roche-Newton, Ilya D. Shkredov
Publikováno v:
Journal of Number Theory. 201:124-134
This note proves that there exists positive constants c 1 and c 2 such that for all finite A ⊂ R with | A + A | ≤ | A | 1 + c 1 we have | A A A | ≫ | A | 2 + c 2 .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9cdf1eafefa5ee796e64c1f9e8240f59
https://doi.org/10.1016/j.jnt.2019.02.026
https://doi.org/10.1016/j.jnt.2019.02.026
Publikováno v:
Annals of Combinatorics. 23:183-205
Balog and Wooley have recently proved that any subset $${\mathcal {A}}$$ of either real numbers or of a prime finite field can be decomposed into two parts $${\mathcal {U}}$$ and $${\mathcal {V}}$$ , one of small additive energy and the other of smal
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::72e9b5172f2aa30810b37954c72de1cd
https://doi.org/10.1007/s00026-019-00420-3
https://doi.org/10.1007/s00026-019-00420-3
Publikováno v:
Mathematika. 65:831-850
We prove that, for any finite set $A \subset \mathbb Q$ with $|AA| \leq K|A|$ and any positive integer $k$, the $k$-fold product set of the shift $A+1$ satisfies the bound $$| \{(a_1+1)(a_2+1) \cdots (a_k+1) : a_i \in A \}| \geq \frac{|A|^k}{(8k^4)^{
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3445fab741e71cbae24e9e0533a0aaa4
https://doi.org/10.1112/s0025579319000081
https://doi.org/10.1112/s0025579319000081
Autor:
Oliver Roche-Newton, Audie Warren
Publikováno v:
European Journal of Combinatorics. 103:103512
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::63c97cb1ee7ffbe68e1d950d35cc447b
https://doi.org/10.1016/j.ejc.2022.103512
https://doi.org/10.1016/j.ejc.2022.103512
Autor:
Audie Warren, Oliver Roche-Newton
We give a construction of a set $$A \subset \mathbb N$$ such that any subset $${A' \subset A}$$ with $$|A'| \gg |A|^{2/3}$$ is neither an additive nor multiplicative Sidon set. In doing so, we refute a conjecture of Klurman and Pohoata.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::986da3e7df39e75e518eea12cdd3835b
http://arxiv.org/abs/2103.13066
http://arxiv.org/abs/2103.13066
Autor:
Oliver Roche-Newton
Let $A \subset \mathbb R$ and $G \subset A \times A$. We prove that, for any $\lambda \in \mathbb R \setminus \{-1,0,1\}$, \[ \max \{|A+_G A|, |A+_G \lambda A|, |A\cdot_G A|\} \gg |G|^{6/11}. \]
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6c8eb75b21787305ef59668d3b0562c5
http://arxiv.org/abs/2010.02050
http://arxiv.org/abs/2010.02050