Sum-product theorems and incidence geometry
Copyright policy ) Chang, Mei-Chu; Solymosi, József;
Sum-product theorems and incidence geometry
In this paper we prove the following theorems in incidence geometry. The main ingredients used are the subspace theorem, Balog–Szemerédi–Gowers Theorem, and Szemerédi–Trotter Theorem. We also generalize the theorems to high dimensions, extend Theorem 1 to \Bbb F_p^2 , and give the version of Theorem 2 over \Bbb Q .
- University of British Columbia Canada
- University of California, Riverside United States
Arithmetic combinatorics; higher degree uniformity, Additive bases, including sumsets, Linear incidence geometry
Arithmetic combinatorics; higher degree uniformity, Additive bases, including sumsets, Linear incidence geometry
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
selected citations
Citations provided by BIP!
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
Citations provided by BIP!popularityPopularity provided by BIP!
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
Popularity provided by BIP! 3
Average
Average
Average
gold
Fields of Science