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Gill, Nick; Helfgott, Harald A. and Rudnev, Misha
(2015).
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 or
, 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.