The geometric case of the Erdős similarity conjecture
We prove the geometric-progression case of the Erdős similarity conjecture. For every fixed $q\in(0,1)$ and every $\eta\in(0,1)$, we construct a compact set $E_{q,\eta}\subseteq[0,1]$ of measure greater than $1-\eta$ containing no nontrivial affine copy of $\{q^n:n\ge1\}$, for any translation and either sign of nonzero dilation. The set may depend on q ; the result makes no simultaneous assertion for different ratios.
Comments and reviews
No comments yet.
API
curl /api/v1/records/openai-math/The-geometric-case-of-the-Erdos-similarity-conjecture
curl -X POST /api/v1/records/openai-math/The-geometric-case-of-the-Erdos-similarity-conjecture/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/The-geometric-case-of-the-Erdos-similarity-conjecture/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'