On growth in an abstract plane

Gill, Nick; Helfgott, Harald A. and Rudnev, Misha (2015). On growth in an abstract plane. Proceedings of the American Mathematical Society, 143(8) pp. 3593–3602.

DOI: https://doi.org/10.1090/proc/12309

Abstract

There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over $\mathbb{R}$ or $\mathbb{C}$, geometric statements on growth often have geometric proofs, what little is known over finite fields rests on arithmetic proofs.

We discuss strategies for geometric proofs of growth over finite fields, and show that growth can be defined and proven in an abstract projective plane -- even one with weak axioms.

Viewing alternatives

Look up in Google Scholar

Download history

Metrics

Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions

Item Actions

Export

About

CORE (COnnecting REpositories)