Zobrazeno 1 - 10
of 208
pro vyhledávání: '"Best, Alex"'
Autor:
Brasca, Riccardo, Birkbeck, Christopher, Boidi, Eric Rodriguez, Best, Alex, van De Velde, Ruben, Yang, Andrew
We formalize a complete proof of the regular case of Fermat's Last Theorem in the Lean4 theorem prover. Our formalization includes a proof of Kummer's lemma, that is the main obstruction to Fermat's Last Theorem for regular primes. Rather than follow
Externí odkaz:
http://arxiv.org/abs/2410.01466
Autor:
Best, Alex, Singh, Prerna
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 during the Covid-19 pandemic. However, these studies have had differing con
Externí odkaz:
http://arxiv.org/abs/2306.09768
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 important 19th century result that motivated the development of modern a
Externí odkaz:
http://arxiv.org/abs/2305.08955
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 $y^2=x^3+d$, where $d$ is a (given) nonzero integer number and all solutions in integers $x$ and $y$
Externí odkaz:
http://arxiv.org/abs/2209.15492
Autor:
Best, Alex J.
We give algorithms to compute Coleman integrals on superelliptic curves over unramified extensions of the p-adics, and apply these via Chabauty methods to determine the set of rational points on such curves. We also determine the solution to an expli
Externí odkaz:
https://hdl.handle.net/2144/43150
Autor:
Best, Alex J., Betts, L. Alexander, Kumpitsch, Theresa, Lüdtke, Martin, McAndrew, Angus W., Qian, Lie, Studnia, Elie, Xu, Yujie
In [Kim05], Kim gave a new proof of Siegel's Theorem that there are only finitely many $S$-integral points on $\mathbb P^1_{\mathbb Z}\setminus\{0,1,\infty\}$. One advantage of Kim's method is that it in principle allows one to actually find these po
Externí odkaz:
http://arxiv.org/abs/2106.10145
Autor:
Best, Alex J., Matschke, Benjamin
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 that the database is likely to be the complete set of such curves. Moreo
Externí odkaz:
http://arxiv.org/abs/2007.10535
Autor:
Best, Alex J., Betts, L. Alexander, Bisatt, Matthew, van Bommel, Raymond, Dokchitser, Vladimir, Faraggi, Omri, Kunzweiler, Sabrina, Maistret, Céline, Morgan, Adam, Muselli, Simone, Nowell, Sarah
A new approach has been recently developed to study the arithmetic of hyperelliptic curves $y^2=f(x)$ over local fields of odd residue characteristic via combinatorial data associated to the roots of $f$. Since its introduction, numerous papers have
Externí odkaz:
http://arxiv.org/abs/2007.01749
Autor:
Best, Alex J., Bober, Jonathan, Booker, Andrew R., Costa, Edgar, Cremona, John, Derickx, Maarten, Lee, Min, Lowry-Duda, David, Roe, David, Sutherland, Andrew V., Voight, John
Publikováno v:
Arithmetic Geometry, Number Theory, and Computation, Simons Symp. (2021), 131-213
We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).
Comment: 63 pages; minor edits, including a correction to Conjecture 8.5.1
Comment: 63 pages; minor edits, including a correction to Conjecture 8.5.1
Externí odkaz:
http://arxiv.org/abs/2002.04717
Autor:
Balakrishnan, Jennifer S., Best, Alex J., Bianchi, Francesca, Lawrence, Brian, Müller, J. Steffen, Triantafillou, Nicholas, Vonk, Jan
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 usually called the method of Chabauty--Kim or non-abelian Chabauty in the l
Externí odkaz:
http://arxiv.org/abs/1910.12755