$ABC$ sum-product theorems for Katz-Tao sets
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912693380710400 |
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| author | Orponen, Tuomas |
| author_facet | Orponen, Tuomas |
| contents | I prove two variants of the $ABC$ sum-product theorem for $δ$-separated sets $A,B,C \subset [0,1]$ satisfying Katz-Tao spacing conditions. The main novelty is that the cardinality of the sets $B,C$ need not match their non-concentration exponent. The new $ABC$ theorems are sharp under their respective hypotheses, and imply the previous one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $ABC$ sum-product theorems for Katz-Tao sets Orponen, Tuomas Combinatorics Classical Analysis and ODEs 11B30, 28A80 I prove two variants of the $ABC$ sum-product theorem for $δ$-separated sets $A,B,C \subset [0,1]$ satisfying Katz-Tao spacing conditions. The main novelty is that the cardinality of the sets $B,C$ need not match their non-concentration exponent. The new $ABC$ theorems are sharp under their respective hypotheses, and imply the previous one. |
| title | $ABC$ sum-product theorems for Katz-Tao sets |
| topic | Combinatorics Classical Analysis and ODEs 11B30, 28A80 |
| url | https://arxiv.org/abs/2511.05091 |