SIAM Journal on Discrete Mathematics
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB

 SIAM J. Discrete Math., 2013, Volume 27, Issue 2, Pages 973–990 (Mi sjdm2)

On new sum-product estimates

S. Konyagina, M. Rudnevb

a Steklov Mathematical Institute, 8 Gubkin Street, Moscow 119991, Russia
b Department of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom

Abstract: New lower bounds involving sum, difference, product, and ratio sets of a set $A\subset {\mathbb C}$ 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 Szemerédi–Trotter theorem with an arithmetic combinatorics technique.

 Funding Agency Grant Number Russian Foundation for Basic Research 11-01-00329 Ministry of Education and Science of the Russian Federation Nsh-6003.2012.1 This author's work was partially supported by the Russian Fund for Basic Research, grant 11-01-00329, and by the Program Supporting Leading Scientific Schools, grant Nsh-6003.2012.1.

DOI: https://doi.org/10.1137/120886418

Bibliographic databases:

MSC: 68R05, 11B75
Revised: 06.03.2013
Language: