Paper Info
Title
On New Sum-Product-Type Estimates.
Abstract
New lower bounds involving sum, difference, product, and ratio sets of a set A subset of C are given. The estimates involving the sum set match, up to constants, the state-of-the-art estimates, proven by Solymosi for the reals and are obtained by generalizing his approach to the complex plane. The bounds involving the difference set improve the currently best known ones, also due to Solymosi, in both the real and complex cases by means of combining the Szemeredi-Trotter theorem with an arithmetic combinatorics technique.
Year
DOI
Venue
2013
10.1137/120886418
SIAM JOURNAL ON DISCRETE MATHEMATICS
Keywords
Field
DocType
Erdos-Szemeredi conjecture,sum-product estimates,Szemeredi-Trotter theorem,incidence theory
Discrete mathematics,Combinatorics,Arithmetic combinatorics,Difference set,Product type,Complex plane,Mathematics
Journal
Volume
Issue
ISSN
27
2
0895-4801
Citations 
PageRank 
References 
5
0.87
6
Authors
2
Name
Order
Citations
PageRank
Sergei V. Konyagin182.10
Misha Rudnev2133.41