5 citations · 8 across the 6 of their papers we have counts for
8 papers · 1 filter
Computing p-adic heights on hyperelliptic curves
Stevan Gajović, J. Steffen Müller
We describe an algorithm to compute the local Coleman-Gross p-adic height at p on a hyperelliptic curve. Previously, this was only possible using an algorithm due to Balakrishnan a…
Linear and quadratic Chabauty for affine hyperbolic curves
Marius Leonhardt, Martin Lüdtke, J. Steffen Müller
We give sufficient conditions for finiteness of linear and quadratic refined Chabauty-Kim loci of affine hyperbolic curves. We achieve this by constructing depth quotients…
Rational points on
Vishal Arul, J. Steffen Müller
We compute the rational points on the Atkin-Lehner quotient using the quadratic Chabauty method. Our work completes the study of exceptional rational points on the cur…
Quadratic Chabauty for modular curves: Algorithms and examples
Jennifer S. Balakrishnan, Netan Dogra, Jan Steffen Müller +2
We describe how the quadratic Chabauty method may be applied to explicitly determine the set of rational points on modular curves of genus whose Jacobians have Mordell--Weil…
Two recent p-adic approaches towards the (effective) Mordell conjecture
Jennifer S. Balakrishnan, Alex J. Best, Francesca Bianchi +4
We give an introductory account of two recent approaches towards an effective proof of the Mordell conjecture, due to Lawrence--Venkatesh and Kim. The latter method, which is usual…
Archimedean local height differences on elliptic curves
J. Steffen Müller, Corinna Stumpe
To compute generators for the Mordell-Weil group of an elliptic curve over a number field, one needs to bound the difference between the naive and the canonical height from above.…
Explicit Chabauty-Kim for the Split Cartan Modular Curve of Level 13
Jennifer S. Balakrishnan, Netan Dogra, J. Steffen Müller +2
We extend the explicit quadratic Chabauty methods developed in previous work by the first two authors to the case of non-hyperelliptic curves. This results in an algorithm to compu…
A height inequality for rational points on elliptic curves implied by the abc-conjecture
Ulf Kühn, J. Steffen Müller
In this short note we show that the uniform abc-conjecture over number fields puts strong restrictions on the coordinates of rational points on elliptic curves. For the proof we us…