1. Incidences of Möbius Transformations in Fp.
- Author
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Warren, Audie and Wheeler, James
- Subjects
- *
DISCRETE geometry , *POINT set theory , *FINITE fields - Abstract
We develop the methods used by Rudnev and Wheeler (2022) to prove an incidence theorem between arbitrary sets of Möbius 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 Möbius transformations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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