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

作者：Thang Pham^*; Tait Michael; Timmons Craig; Le Anh Vinh

来源：Journal of Combinatorial Theory - Series A, 2017, 147: 55-74.

DOI：10.1016/j.jcta.2016.11.003

• Szemeredi-Trotter theorem
• Quasifield
• Sum-product estimate

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.

• 出版日期2017-4