New results on sums and products in ℝ
| Autor: | I. D. Shkredov, S. V. Konyagin |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Inequality media_common.quotation_subject 010102 general mathematics Multiplicative function Cartesian product 01 natural sciences Combinatorics symbols.namesake Mathematics (miscellaneous) 0103 physical sciences symbols 010307 mathematical physics 0101 mathematics Mathematics media_common |
| Zdroj: | Proceedings of the Steklov Institute of Mathematics. 294:78-88 |
| ISSN: | 1531-8605 0081-5438 |
| DOI: | 10.1134/s0081543816060055 |
| Popis: | We improve previous sum–product estimates in ℝ; namely, we prove the inequality max{|A + A|, |AA|} ≫ |A|4/3+c, where c is any number less than 5/9813. New lower bounds for sums of sets with small product set are found. We also obtain results on the additive and multiplicative energies; in particular, we improve a result of Balog and Wooley. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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