A Szemerédi–Trotter type theorem, sum-product estimates in finite quasifields, and related results

Authors: Phạm Văn Thắng, Michael Tait, Craig Timmons, Lê Anh Vinh,

https://doi.org/10.1016/j.jcta.2016.11.003

Publisher, magazine: ,

Publication year: 2017

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Abstract

We prove a Szemerédi–Trotter type theorem and a sum-product estimate in the setting of finite quasifields. These estimates generalize results of the fourth author, of Garaev, and of Vu. We generalize results of Gyarmati and Sárközy on the solvability of the equations and over a finite field. Other analogous results that are known to hold in finite fields are generalized to finite quasifields.

Tags: Szemerédi–Trotter theoremQuasifieldSum-product estimate