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math.NT2023
Bounds for rational points on algebraic curves, optimal in the degree, and dimension growth
Gal Binyamini, Raf Cluckers, Dmitry Novikov
Bounding the number of rational points of height at most on irreducible algebraic plane curves of degree has been an intense topic of investigation since the work by Bombie…
math.NT2023
An effective Pila-Wilkie theorem for sets definable using Pfaffian functions, with some diophantine applications
Gal Binyamini, Gareth O. Jones, Harry Schmidt +1
We prove an effective version of the Pila-Wilkie Theorem for sets definable using Pfaffian functions, providing effective estimates for the number of algebraic points of bounded he…