19 citations · 32 across the 9 of their papers we have counts for
10 papers
Comparing intervention measures in a model of a disease outbreak on a university campus
Alex Best, Prerna Singh
A number of theoretical models have been developed in recent years modelling epidemic spread in educational settings such as universities to help inform re-opening strategies durin…
Fermat's Last Theorem for regular primes
Alex J. Best, Christopher Birkbeck, Riccardo Brasca +1
We formalise the proof of the first case of Fermat's Last Theorem for regular primes using the \emph{Lean} theorem prover and its mathematical library \emph{mathlib}. This is an im…
Formalized Class Group Computations and Integral Points on Mordell Elliptic Curves
Anne Baanen, Alex J. Best, Nirvana Coppola +1
Diophantine equations are a popular and active area of research in number theory. In this paper we consider Mordell equations, which are of the form , where is a (gi…
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…
Computing Zeta Functions of Cyclic Covers in Large Characteristic
Vishal Arul, Alex J. Best, Edgar Costa +2
We describe an algorithm to compute the zeta function of a cyclic cover of the projective line over a finite field of characteristic that runs in time . We conf…