# An improved point‐line incidence bound over arbitrary fields

@article{Stevens2017AnIP, title={An improved point‐line incidence bound over arbitrary fields}, author={S. Stevens and F. D. Zeeuw}, journal={Bulletin of The London Mathematical Society}, year={2017}, volume={49}, pages={842-858} }

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<n<m8/7, determine at most O(m11/15n11/15) incidences (where, if F has positive characteristic p, we assume m−2n13≪p15). This improves on the previous best-known bound, due to Jones.
To obtain our bound, we first prove an optimal point-line incidence bound on… Expand

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