AN EXPLICIT INCIDENCE THEOREM IN

DOI10.1112/S0025579310001208zbMath1264.11016arXiv1001.1980OpenAlexW3102580705MaRDI QIDQ3074009

Michael Rudnev, Harald Andrés Helfgott

Publication date: 14 February 2011

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1980

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (21)

Szemer\'{e}di-Trotter type results in arbitrary finite fields ⋮ Areas of triangles and Beck's theorem in planes over finite fields ⋮ Conditional expanding bounds for two-variable functions over finite valuation rings ⋮ On the concentration of points of polynomial maps and applications ⋮ An improved incidence bound for fields of prime order ⋮ Pinned algebraic distances determined by Cartesian products in 𝔽_{𝕡}² ⋮ Elementary methods for incidence problems in finite fields ⋮ On distinct perpendicular bisectors and pinned distances in finite fields ⋮ Improved incidence bounds over arbitrary finite fields via the VC-dimension theory ⋮ Incidences between planes over finite fields ⋮ New restriction estimates for the 3-d paraboloid over finite fields ⋮ A Szemerédi-Trotter type theorem, sum-product estimates in finite quasifields, and related results ⋮ A modular Szemerédi-Trotter theorem for hyperbolas ⋮ Conditional expanding bounds for two-variable functions over prime fields ⋮ AN EXPLICIT TWO‐SOURCE EXTRACTOR WITH MIN‐ENTROPY RATE NEAR ⋮ Fp is locally like ℂ ⋮ Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition ⋮ A point-conic incidence bound and applications over \(\mathbb{F}_p\) ⋮ Bounds of trilinear and quadrilinear exponential sums ⋮ Variations on the Sum-Product Problem ⋮ On growth in an abstract plane

Cites Work

• On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry
• Extremal problems in discrete geometry
• Multilinear exponential sums in prime fields under optimal entropy condition on the sources
• A sum-product estimate in finite fields, and applications
• A slight improvement to Garaev's sum product estimate
• On a variant of sum-product estimates and explicit exponential sum bounds in prime fields

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