P. Habegger

activity

20112021

most citedThe Tate-Voloch Conjecture in a Power of a Modular Curve

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

collaborators

6 papers

math.NT2021

Lower Bounds for the Canonical Height of a Unicritical Polynomial and Capacity

Philipp Habegger, Harry Schmidt

In a recent breakthrough, Dimitrov solved the Schinzel-Zassenhaus Conjecture. We follow his approach and adapt it to certain dynamical systems arising from polynomials of the form…

math.NT2020

Uniformity in Mordell-Lang for curves

Vesselin Dimitrov, Ziyang Gao, Philipp Habegger

Consider a smooth, geometrically irreducible, projective curve of genus $g \geq 2$ defined over a number field of degree $d \geq 1$ . It has at most finitely many rational points by t…

math.NT2019

Uniform bound for the number of rational points on a pencil of curves

Vesselin Dimitrov, Ziyang Gao, Philipp Habegger

Consider a one-parameter family of smooth, irreducible, projective curves of genus $g \geq 2$ defined over a number field. Each fiber contains at most finitely many rational points b…

math.NT2018

No singular modulus is a unit

Yu. Bilu, P. Habegger, L. Kühne

A result of the second-named author states that there are only finitely many CM-elliptic curves over $C$ whose $j$ -invariant is an algebraic unit. His proof depends on Duk…

math.NT2012★ 1 cited

The Tate-Voloch Conjecture in a Power of a Modular Curve

Philipp Habegger

Let $p$ be a prime. Tate and Voloch proved that a point of finite order in the algebraic torus cannot be $p$ -adically too close to a fixed subvariety without lying on it. The curre…

math.NT2011

Torsion Points on Elliptic Curves in Weierstrass Form

Philipp Habegger

We prove that there are only finitely many complex numbers $a$ and $b$ with $4 a^{3} + 27 b^{2} \neq = 0$ such that the three points $(1, *), (2, *),$ and $(3, *)$ are simultaneously torsion on t…