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On sets with small additive doubling in product sets

Dmitrii Zhelezov (Institutionen för matematiska vetenskaper, matematik)
Journal of Number Theory (0022-314X). Vol. 157 (2015), p. 170-183.
[Artikel, refereegranskad vetenskaplig]

Text: Following the sum-product paradigm, we prove that for a set B of polynomial growth, the product set B.B cannot contain large subsets with small doubling and size of order |B|2. It follows that the additive energy of B.B is asymptotically o(|B|6). In particular, we extend to sets with small doubling and of polynomial growth the classical Multiplication Table theorem of Erdos which says that |[1. . .n].[1. . .n]|=o(n2).

Nyckelord: Additive energy , Generalized arithmetic progressions , Prime divisors , Product sets

Denna post skapades 2015-07-27. Senast ändrad 2016-11-07.
CPL Pubid: 219982


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