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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.LO2018
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…
math.NT2018
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…