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- W4303579655 abstract "For $p$ being a large prime number, and $A subset mathbb{F}_p$ we prove the following: $(i)$ If $A(A+A)$ does not cover all nonzero residues in $mathbb{F}_p$, then $|A| < p/8 + o(p)$. $(ii)$ If $A$ is both sum-free and satisfies $A = A^*$, then $|A| < p/9 + o(p)$. $(iii)$ If $|A| gg frac{loglog{p}}{sqrt{log{p}}}p$, then $|A + A^*| geqslant (1 - o(1))min(2sqrt{|A|p}, p)$. Here the constants $1/8$, $1/9$, and $2$ are the best possible. The proof involves emph{wrappers}, subsets of a finite abelian group $G$, with which we `wrap' popular values in convolutions $A * B$ for dense sets $A, B subseteq G$. These objects carry some special structural features, making them capable of addressing both additive-combinatorial and enumerative problems." @default.
- W4303579655 created "2022-10-08" @default.
- W4303579655 creator A5055884833 @default.
- W4303579655 date "2020-11-23" @default.
- W4303579655 modified "2023-09-27" @default.
- W4303579655 title "A new bound for $A(A + A)$ for large sets" @default.
- W4303579655 doi "https://doi.org/10.48550/arxiv.2011.11468" @default.
- W4303579655 hasPublicationYear "2020" @default.
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