An explicit incidence theorem in p
By Harald Andrés Helfgott, M. Rudnev. 2010
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Let P = A × A ⊂𝔽 p ×𝔽 p , p a prime. Assume that P = A × A has n elements, n p . See P as a set of points in the plane over 𝔽 p . We show that the pairs of points in P determine lines, where c is an absolute constant. We derive from this an incidence theorem: the number of incidences between a set of n points and a set of n lines in the projective plane over 𝔽 p ( n p ) is bounded by , where C is an absolute constant.
Subfields: Computational Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/7741f7f7d947dabda4d92472b476fd07ab2c4304
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In Computational Mathematics
In Discrete Mathematics and Combinatorics
Citations in the corpus
- An improved point‐line incidence bound over arbitrary fields (2016, methodology): “In F2p, Helfgott and Rudnev [18] established that if m p and P = A×A (so no line has Ω(m) points), then P determines Ω(m1+1/267) lines.”