G. Jones

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20172020

most citedInteger Valued Definable Functions in

R_{an, e x p}

1 citations · 1 across the 2 of their papers we have counts for

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math.NT2020

On algebraic values of Weierstrass $σ$ -functions

Gareth Boxall, Taboka Chalebgwa, Gareth Jones

Suppose that $Ω$ is a lattice in the complex plane and let $σ$ be the corresponding Weierstrass $σ$ -function. Assume that the point $τ$ associated to $Ω$ in the standard fundamenta…

math.NT2020★ 1 cited

Integer Valued Definable Functions in $R_{an, e x p}$

Gareth Jones, Shi Qiu

We give two variations on a result of Wilkie's on unary functions defianble in $R_{an, e x p}$ that take integer values at positive integers. Provided that the functions gro…

math.NT2018

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…

math.NT2017

Pfaffian definitions of Weierstrass elliptic functions

Gareth Jones, Harry Schmidt

We give explicit definitions of the Weierstrass elliptic functions $℘$ and $ζ$ in terms of pfaffian functions, with complexity independent of the lattice involved. We also give s…

On algebraic values of Weierstrass σ-functions

Integer Valued Definable Functions in Ran,exp​

Rational values of transcendental functions and arithmetic dynamics

Pfaffian definitions of Weierstrass elliptic functions

On algebraic values of Weierstrass $σ$ -functions

Integer Valued Definable Functions in $R_{an, e x p}$