20 citations · 34 across the 5 of their papers we have counts for
6 papers
Constructions for the Elekes-Szabó and Elekes-Rónyai problems
Mehdi Makhul, Oliver Roche-Newton, Audie Warren +1
We give a construction of a non-degenerate polynomial and a set of cardinality such that $\left|Z(F)\cap (A \times A \times A) \right| \gg n^{\frac{…
Ordinary lines in space
Frank de Zeeuw
We prove that if a finite point set in real space does not have too many points on a plane, then it spans a quadratic number of ordinary lines. This answers the real case of a ques…
Spanned lines and Langer's inequality
Frank de Zeeuw
We collect some results in combinatorial geometry that follow from an inequality of Langer in algebraic geometry. Langer's inequality gives a lower bound on the number of incidence…
A short proof of Rudnev's point-plane incidence bound
Frank de Zeeuw
In this note we give a shortened proof of a theorem of Rudnev, which bounds the number of incidences between points and planes over an arbitrary field. Rudnev's proof uses a map th…
On the number of ordinary circles
Hossein Nassajian Mojarrad, Frank de Zeeuw
We prove that any points in , not all on a line or circle, determine at least ordinary circles (circles containing exactly three of the …
Distinct values of bilinear forms on algebraic curves
Claudiu Valculescu, Frank de Zeeuw
Let be a bilinear form on pairs of points in the complex plane, of the form , for an invertible complex matrix . We prove that any finite set …