2015/05/27 by Thang Pham, Michael Tait, Pham, Thang +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT
paper · pdf · doi:10.48550/arxiv.1505.07308
Referee suggestions included. To appear in Journal of Combinatorial Theory, Series A
arxiv created 2016/10/19 · arxiv updated 2016/10/20
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 a + b = cd and ab + 1 = cd over a finite field. Other analogous results that are known to hold in finite fields are generalized to finite quasifields.