26 citations · 37 across the 7 of their papers we have counts for
7 papers
Fermat's Four Squares Theorem
Alf van der Poorten
It is easy to find a right-angled triangle with integer sides whose area is 6. There is no such triangle with area 5, but there is one with rational sides (a `\emph{Pythagorean tri…
Hyperelliptic curves, continued fractions, and Somos sequences
Alfred J. van der Poorten
We detail the continued fraction expansion of the square root of a monic polynomials of even degree. We note that each step of the expansion corresponds to addition of the divisor…
Genus 2 curves, continued fractions, and Somos sequences
Alfred J. van der Poorten
We detail the continued fraction expansion of the square root of monic sextic polynomials. We note in passing that each line of the expansion corresponds to addition of the divisor…
Quadratic irrational integers with partly prescribed continued fraction expansion
Alfred J. van der Poorten
We generalise remarks of Euler and of Perron by explaining how to detail all quadratic irrational integers for which the symmetric part of the period of their continued fraction ex…
Specialisation and reduction of continued fractions of formal power series
Alfred J. van der Poorten
We discuss and illustrate the behaviour of the continued fraction expansion of a formal power series under specialisation of parameters or their reduction modulo and sketch som…
Pseudo-elliptic integrals, units, and torsion
Francesco Pappalardi, Alfred J. van der Poorten
We remark on pseudo-elliptic integrals and on exceptional function fields, namely function fields defined over an infinite base field but nonetheless containing non-trivial units.…