A modular Szemerédi-Trotter theorem for hyperbolas

DOI10.1016/j.crma.2012.09.011zbMath1272.11024arXiv1208.4008OpenAlexW2964274337MaRDI QIDQ1759772

Jean Bourgain

Publication date: 22 November 2012

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.4008

zbMATH Keywords

finite fieldsSzemerédi-Trotter theoremspecial linear group

Mathematics Subject Classification ID

Finite fields and commutative rings (number-theoretic aspects) (11T99) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (9)

Non-commutative methods in additive combinatorics and number theory ⋮ Incidences of Möbius transformations in \(\mathbb{F}_p\) ⋮ Arithmetic and dynamics on varieties of Markoff type ⋮ Popular products and continued fractions ⋮ Modular hyperbolas and bilinear forms of Kloosterman sums ⋮ On asymptotic formulae in some sum–product questions ⋮ Markoff triples and strong approximation ⋮ On incidence bounds with Möbius hyperbolae in positive characteristic ⋮ A point-conic incidence bound and applications over \(\mathbb{F}_p\)

Cites Work

• Bounds for multiplicities of automorphic representations
• A sum-product estimate in finite fields, and applications
• Growth and generation in \(\text{SL}_2(\mathbb{Z}/p\mathbb{Z})\).
• Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
• AN EXPLICIT INCIDENCE THEOREM IN
• MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS

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