49 citations · 161 across the 26 of their papers we have counts for
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math.NT2008
Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group
Patrick Ingram
Let be an elliptic surface over the curve , defined over a number field , let be a section of , and let be a rational prime. For any non-singular fibre $E_t…
math.NT2008★ 3 cited
Uniform Bounds on Pre-Images under Quadratic Dynamical Systems
Xander Faber, Benjamin Hutz, Patrick Ingram +4
For any elements b,c of a number field K, let G(b,c) denote the backwards orbit of b under the map f_c: C-->C given by f_c(x)=x^2+c. We prove an upper bound on the number of elemen…
math.NT2008★ 1 cited
Multiples of integral points on elliptic curves
Patrick Ingram
If is a minimal elliptic curve defined over $\ZZ$, we obtain a bound , depending only on the global Tamagawa number of , such that for any point $P\in E(\QQ)$, is in…