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