An improved point‐line incidence bound over arbitrary fields

By Sophie Stevens, Frank de Zeeuw. 2016

118 citations recorded by the source corpus.

We prove a new upper bound for the number of incidences between points and lines in a plane over an arbitrary field F , a problem first considered by Bourgain, Katz and Tao. Specifically, we show that m points and n lines in F2 , with m7/8

Subfields: Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/293a34c5467f2c764cd0939911d778e48d96c0a1

How researchers see this paper

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In Computational Theory and Mathematics

1. Ilya D. Shkredov
2. M. Rudnev
3. Oliver Roche-Newton
4. Brendan Murphy
5. Giorgis Petridis
6. Sophie Stevens

In Computer Graphics and Computer-Aided Design

1. Ilya D. Shkredov
2. Oliver Roche-Newton
3. Brendan Murphy
4. Giorgis Petridis
5. M. Rudnev
6. Sophie Stevens

In Discrete Mathematics and Combinatorics

1. Ilya D. Shkredov
2. M. Rudnev
3. Brendan Murphy
4. Oliver Roche-Newton
5. Giorgis Petridis
6. Sophie Stevens
7. Frank de Zeeuw
8. Tom Sanders

Citations in the corpus

• NEW RESULTS ON SUM‐PRODUCT TYPE GROWTH OVER FIELDS (2017, background): “Pham, Vinh, and de Zeeuw [30] showed that a large class of quadratic polynomials f in three variables satisfy the expansion bound |f(A)| ≫ min{p, |A|3/2}.”