Arithmetic combinatorics; higher degree uniformity
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Sum-product problems (AlphaEvolve problem 45). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.
Furstenberg-Sárközy Problem (AlphaEvolve problem 31). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.
The Arithmetic Kakeya Conjecture (AlphaEvolve problem 30). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.
Sum-product exponent for the reals: determine C 84b or improve its bounds; the repository records frac 4 3 + frac 10 4407 approx 1.3356 (lower) and <2 (1.999281 ) (upper).
Marton's conjecture constant (PFR): determine C 18 or improve its bounds; the repository records 1 (lower) and 9 (upper).
Furstenberg–Sárközy square-difference constant: determine C 4b or improve its bounds; the repository records 0.758068 (lower) and 1 (upper).
The Arithmetic Kakeya Conjecture. Solid result problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.
These are selected sources for the parent class. Article coverage is a first reviewed selection, and may not cover this exact subcategory.
Mathematical Sciences Publishers
Algebra, number theory and their connections
European Mathematical Society / EMS Press
Mathematical surveys
2019 · 3 questions extracted
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