6 citations · 6 across the 4 of their papers we have counts for
7 papers · 1 filter
Refined Selmer equations for the thrice-punctured line in depth two
Alex J. Best, L. Alexander Betts, Theresa Kumpitsch +5
In [Kim05], Kim gave a new proof of Siegel's Theorem that there are only finitely many -integral points on . One advantage of Kim…
Elliptic curves with good reduction outside of the first six primes
Alex J. Best, Benjamin Matschke
We present a database of rational elliptic curves, up to Q-isomorphism, with good reduction outside {2,3,5,7,11,13}. We provide a heuristic involving the abc and BSD conjectures th…
A user's guide to the local arithmetic of hyperelliptic curves
Alex J. Best, L. Alexander Betts, Matthew Bisatt +8
A new approach has been recently developed to study the arithmetic of hyperelliptic curves over local fields of odd residue characteristic via combinatorial data associa…
Computing classical modular forms
Alex J. Best, Jonathan Bober, Andrew R. Booker +8
We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).
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…
Explicit Coleman Integration in Larger Characteristic
Alex J. Best
We describe a more efficient algorithm to compute p-adic Coleman integrals on odd degree hyperelliptic curves for large primes p. The improvements come from using fast linear recur…