Incidences of Möbius transformations in ${\mathbb{F}}_p$

Abstract

We develop the methods used by Rudnev and Wheeler to prove an incidence theorem between arbitrary sets of Möbius transformations and point sets in ${\mathbb{F}}_p^2$. We also note some asymmetric incidence results, and give applications of these results to various problems in additive combinatorics and discrete geometry.

12 pages

References in corpus (3)

• An Improved Point-Line Incidence Bound Over Arbitrary Fields
• New results on sum-product type growth over fields
• On growth rate in $S{L}_2({\mathbf{F}}_p)$, the affine group and sum-product type implications