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

We prove a Szemeredi-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 Sarkozy 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. (C) 2016 Elsevier Inc. All rights reserved.


Published in:
Journal Of Combinatorial Theory Series A, 147, 55-74
Year:
2017
Publisher:
San Diego, Academic Press Inc Elsevier Science
ISSN:
0097-3165
Keywords:
Laboratories:




 Record created 2017-03-27, last modified 2018-09-13


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