16 citations · 26 across the 4 of their papers we have counts for
5 papers
Combinatorial Applications of the Subspace Theorem
Ryan Schwartz, Jozsef Solymosi
The Subspace Theorem is a powerful tool in number theory. It has appeared in various forms and been adapted and improved over time. It's applications include diophantine approximat…
Using the subspace theorem to bound unit distances
Ryan Schwartz
We prove a special case of Erdős' unit distance problem using a corollary of the subspace theorem bounding the number of solutions of linear equations from a multiplicative group.…
Extensions of a result of Elekes and Rónyai
Ryan Schwartz, József Solymosi, Frank de Zeeuw
Many problems in combinatorial geometry can be formulated in terms of curves or surfaces containing many points of a cartesian product. In 2000, Elekes and Rónyai proved that if th…
Rational Distances with Rational Angles
Ryan Schwartz, József Solymosi, Frank de Zeeuw
In 1946 Erd\H os asked for the maximum number of unit distances, , among points in the plane. He showed that and conjectured that this was the…
Simultaneous Arithmetic Progressions on Algebraic Curves
Ryan Schwartz, József Solymosi, Frank de Zeeuw
A simultaneous arithmetic progression (s.a.p.) of length k consists of k points (x_i, y_σ(i)), where x_i and y_i are arithmetic progressions and σis a permutation. Garcia-Selfa and…