8 citations · 18 across the 6 of their papers we have counts for
11 papers
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…
On algebraic values of Weierstrass -functions
Gareth Boxall, Taboka Chalebgwa, Gareth Jones
Suppose that is a lattice in the complex plane and let be the corresponding Weierstrass -function. Assume that the point associated to in the standard fundamenta…
Integer Valued Definable Functions in
Gareth Jones, Shi Qiu
We give two variations on a result of Wilkie's on unary functions defianble in that take integer values at positive integers. Provided that the functions gro…
Pseudo-parabolic category over quaternionic projective plane
Gareth Jones, Andrey Mudrov
Quaternionic projective plane is the next simplest conjugacy class of the symplectic group with pseudo-Levi stabilizer subgroup after the sphere $\mathbb{S…
Rational values of transcendental functions and arithmetic dynamics
Gareth Boxall, Gareth Jones, Harry Schmidt
We count algebraic points of bounded height and degree on the graphs of certain functions analytic on the unit disk, obtaining a bound which is polynomial in the degree and in the…
Effective Pila--Wilkie bounds for unrestricted Pfaffian surfaces
Gareth O. Jones, Margaret E. M. Thomas
We prove effective Pila--Wilkie estimates for the number of rational points of bounded height lying on certain surfaces defined by Pfaffian functions. The class of surfaces to whic…
A Manin-Mumford theorem for the maximal compact subgroup of a universal vectorial extension of a product of elliptic curves
Gareth Jones, Harry Schmidt
We study the intersection of an algebraic variety with the maximal compact subgroup of a universal vectorial extension of a product of elliptic curves. For this intersection we sho…
On local definability of holomorphic functions
Gareth Jones, Jonathan Kirby, Olivier Le Gal +1
Given a collection A of holomorphic functions, we consider how to describe all the holomorphic functions locally definable from A. The notion of local definability of holomorphic f…
Pfaffian definitions of Weierstrass elliptic functions
Gareth Jones, Harry Schmidt
We give explicit definitions of the Weierstrass elliptic functions and in terms of pfaffian functions, with complexity independent of the lattice involved. We also give s…
Six unlikely intersection problems in search of effectivity
P. Habegger, G. Jones, D. Masser
We investigate four properties related to an elliptic curve in Legendre form with parameter : the curve has complex multiplication, has complex multiplica…
Local interdefinability of Weierstrass elliptic functions
Gareth Jones, Jonathan Kirby, Tamara Servi
We explain which Weierstrass elliptic functions are locally definable from other elliptic functions and exponentiation in the context of o-minimal structures. The proofs make use o…