Rado's criterion over squares and higher powers JBAQ7DTW7B
| URI | m2://res/JBAQ7DTW7B |
|---|---|
| Kind | preprint |
| Creators | Sam Chow, Sofia Lindqvist, Sean Prendiville |
| Date | 2018-06-13 |
| MSC | 11-XX, 05-XX |
| Subjects | arxiv math.NT, arxiv math.CO |
| Scope | in |
Expressions
e1: version, preprint
| Language | en |
|---|---|
| Date | 2018-06-13 |
| Ids | arXiv 1806.05002 |
Items in this resource
The mentions of the inventory that name this resource. Each name links to the card of its inventory row.
| Item | Kind | Where | Source |
|---|---|---|---|
| Major arc asymptotic | statement | lemma D.9 | arxiv |
| Functional FGR | statement | lemma 15.2 | arxiv |
| Partition regular | definition | definition 1.2 | arxiv |
| 1XVQSAHDXB | statement | lemma A.2 | arxiv |
| Generalised von Neumann | statement | lemma C.3 | arxiv |
| Supersaturated homogeneous S\'ark\"ozy | statement | theorem 2.4 | arxiv |
| 2Z4WJ0CQKY | statement | lemma A.5 | arxiv |
| $T$ counting operator | definition | definition 4.1 | arxiv |
| Homogeneous Bergelson--Leibman | statement | corollary 9.1 | arxiv |
| Density increment lemma | statement | lemma 7.1 | arxiv |
| 4NSDE7V28Q | statement | lemma 17.2 | arxiv |
| Density transfer | statement | lemma 12.3 | arxiv |
| Density transfer | statement | lemma 6.2 | arxiv |
| Fourier decay | statement | lemma 6.3 | arxiv |
| 5ZHJHC0XZQ | statement | lemma A.4 | arxiv |
| $p$-restriction | definition | definition 5.4 | arxiv |
| $T_1$ counting operator | definition | definition 5.1 | arxiv |
| Schur-type theorem in the squares | statement | theorem 1.1 | arxiv |
| Fragmentation into level sets | statement | lemma 7.4 | arxiv |
| Non-linear Roth--S\'ark\"ozy | statement | theorem 12.1 | arxiv |
| Rado over $k$th powers | statement | theorem 1.3 | arxiv |
| 7RH9DJMXQD | definition | definition | arxiv |
| Fourier decay | definition | definition 5.3 | arxiv |
| 90BRYXPP8K | conjecture | conjecture 3.1 | arxiv |
| Homogeneous set | definition | definition 2.2 | arxiv |
| 9QV78GBZ6R | statement | lemma D.8 | arxiv |
| BTYZNK3C20 | unknown | unknown | arxiv |
| Functional S\'ark\"ozy | statement | lemma 5.2 | arxiv |
| Finitary Schur-type theorem in the squares | statement | theorem 2.1 | arxiv |
| DDFY7NFQJ0 | statement | lemma D.2 | arxiv |
| Second pruning step | statement | lemma D.7 | arxiv |
| DQX8J7HWSE | statement | lemma A.3 | arxiv |
| $R$-smooth numbers | definition | definition A.1 | arxiv |
| EQ0DYHY6Q0 | statement | lemma D.3 | arxiv |
| F10WFKWZ4M | statement | theorem 3.2 | arxiv |
| Pseudorandom Roth--S\'ark\"ozy | statement | theorem 11.4 | arxiv |
| Lefmann + Hardy--Littlewood circle method | statement | theorem 1.8 | arxiv |
| Functional Roth--S\'ark\"ozy | statement | lemma 11.3 | arxiv |
| Homogeneous sets are dense | statement | lemma 4.2 | arxiv |
| Smooth finitary colouring result | statement | theorem 13.1 | arxiv |
| Non-linear homogeneous S\'ark\"ozy | statement | theorem 2.3 | arxiv |
| $R$-smooth numbers | definition | definition 1.6 | arxiv |
| Multidimensional homogeneous S\'ark\"ozy | statement | theorem 2.5 | arxiv |
| Supersaturation in the smooths | statement | theorem 1.7 | arxiv |
| Restriction estimate | statement | lemma 6.4 | arxiv |
| Modelling lemma | statement | proposition 14.1 | arxiv |
| JT32ZKVSR6 | statement | lemma D.10 | arxiv |
| Lefmann | statement | lemma F.1 | arxiv |
| M0C7AK4B2T | statement | lemma F.2 | arxiv |
| Homogeneous counting lemma | statement | lemma 7.2 | arxiv |
| Supersaturated smooth homogeneous Roth--S\'ark\"ozy | statement | theorem 10.1 | arxiv |
| P4GAM9MFD0 | statement | theorem B.1 | arxiv |
| QFD67XN35Z | statement | lemma C.1 | arxiv |
| Lefmann | statement | theorem 1.9 | arxiv |
| Varnavides averaging | statement | theorem 9.2 | arxiv |
| Supersaturation\footnote{The term `supersaturation', from extremal combinatorics, describes when we wish to ``determine the minimum number of copies of a particular substructure in a combinatorial object of prescribed size'' . For us, the substructure is defined by a Diophantine equation.} in squares minus one | statement | theorem 1.4 | arxiv |
| SHPBFZYDSA | statement | lemma 17.1 | arxiv |
| T018DV0TQ3 | statement | lemma E.4 | arxiv |
| Pseudorandom S\'ark\"ozy | statement | theorem 5.5 | arxiv |
| First level | statement | lemma D.1 | arxiv |
| TEBY5HRX7J | statement | lemma C.2 | arxiv |
| V2Q9BA107Z | statement | lemma B.4 | arxiv |
| $T_\ell$ counting operator | definition | definition 11.1 | arxiv |
| Fourier decay | statement | lemma 12.4 | arxiv |
| Fourier decay | statement | lemma 16.1 | arxiv |
| VCWTPXJ2V2 | statement | lemma B.3 | arxiv |
| Restriction estimate | statement | lemma 12.5 | arxiv |
| Restriction estimate | statement | lemma 16.2 | arxiv |
| W9QD623YYK | statement | lemma E.1 | arxiv |
| WNMFKD77XP | statement | statement | arxiv |
| WT6JTH7S10 | statement | lemma F.3 | arxiv |
| X7MF47TGVV | statement | lemma 12.2 | arxiv |
| $T_2$ counting operator | definition | definition 6.1 | arxiv |
| First pruning step | statement | lemma D.6 | arxiv |
| Varnavides argument | statement | proposition 8.1 | arxiv |
| XCVN8XD4F4 | unknown | unknown | arxiv |
| Minor arcs | statement | lemma D.4 | arxiv |
| Pseudorandom FGR | statement | proposition 15.1 | arxiv |
| ZGRJZAQVHR | statement | lemma E.3 | arxiv |
| Generalised von Neumann theorem | statement | lemma 7.3 | arxiv |
Catalogue records
- arxiv: 1806.05002 (work)
- arxiv_text: 1806.05002 (work)