Incidences of Mobius Transformations in Fp

We develop the methods used by Rudnev and Wheeler (2022) to prove an incidence theorem between arbitrary sets of Mobius transformations and point sets in 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. For instance, we give an improvement to a result of Shkredov concerning the number of representations of a non-zero product defined by a set with small sum-set, and a version of Beck's theorem for Mobius transformations.