Areas of triangles and Beck's theorem in planes over finite fields

DOI10.1007/s00493-014-2977-7zbMath1363.52015arXiv1205.0107OpenAlexW2143031211MaRDI QIDQ313454

Yujia Zhai, Alexander Iosevich, Michael Rudnev

Publication date: 9 September 2016

Published in: Combinatorica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.0107

zbMATH Keywords

finite fieldstrianglesBeck's theoremFourier mechanism

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Erd?s problems and related topics of discrete geometry (52C10)

Related Items

Erdős type problems in modules over cyclic rings, Elementary methods for incidence problems in finite fields, Extending Erdős-Beck's theorem to higher dimensions, Beck's theorem for plane curves, Incidences between planes over finite fields, Some combinatorial number theory problems over finite valuation rings, Triangle areas in line arrangements, Incidence Bounds for Block Designs

Cites Work

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• Distinct triangle areas in a planar point set over finite fields
• The Szemerédi-Trotter type theorem and the sum-product estimate in finite fields
• On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry
• Extremal problems in discrete geometry
• On additive properties of product sets in an arbitrary finite field
• Generalized incidence theorems, homogeneous forms and sum-product estimates in finite fields
• 2N noncollinear points determine at least 2N directions
• A sum-product estimate in finite fields, and applications
• On an application of Guth-Katz theorem
• On the volume set of point sets in vector spaces over finite fields
• An Improved Sum–Product Inequality in Fields of Prime Order
• Averages over hyperplanes, sum-product theory in vector spaces over finite fields and the Erdős-Falconer distance conjecture
• AN EXPLICIT INCIDENCE THEOREM IN
• Research Problems in Discrete Geometry
• An improved sum-product estimate for general finite fields
• The sum-product estimate for large subsets of prime fields
• The Minimum Number of Distinct Areas of Triangles Determined by a Set of n Points in the Plane
• Sums and products in finite fields: an integral geometric viewpoint
• Sum-product Estimates in Finite Fields via Kloosterman Sums
• On Sets of Distances of n Points
• On a problem in combinatorial geometry