6 citations · 19 across the 11 of their papers we have counts for
13 papers
Leiden Declaration on Artificial Intelligence and Mathematics
Jarod Alper, Michael Barany, Alain Chavarri Villarello +13
This declaration calls for action to address the challenges posed by the use of artificial intelligence within mathematics research. Technological developments have repeatedly tran…
Formally certifying number field invariants
Alain Chavarri Villarello, Sander R. Dahmen
Number fields, which generalize the rational numbers, are fundamental objects in number theory. Many of their key arithmetic properties are captured by invariants whose computation…
On the generalized Fermat equation
Alex J. Best, Sander R. Dahmen, Nuno Freitas
Let . We study the generalized Fermat equation \[x^{13}+y^{13}=z^n, \quad x,y,z \in \mathbb{Z}, \quad \gcd(x,y,z)=1.\] Using a combination of techniques,…
Certifying rings of integers in number fields
Anne Baanen, Alain Chavarri Villarello, Sander R. Dahmen
Number fields and their rings of integers, which generalize the rational numbers and the integers, are foundational objects in number theory. There are several computer algebra sys…
Explicitly bounding perfect powers in elliptic divisibility sequences
Sander R. Dahmen, Joey M. van Langen
In this paper we consider elliptic divisibility sequences generated by a point on an elliptic curve over with -invariant given by an integral short Weierstra…
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…