X-Nico

3 unusual facts about Noam Elkies


Counting points on elliptic curves

In the 1990s, Noam Elkies, followed by A. O. L. Atkin devised improvements to Schoof's basic algorithm by making a distinction among the primes \ell 1, \ldots, \ell s that are used.

Elkies trinomial curves

In number theory, the Elkies trinomial curves are certain hyperelliptic curves constructed by Noam Elkies which have the property that rational points on them correspond to trinomial polynomials giving an extension of Q with particular Galois groups.

Jacobi–Madden equation

Noam Elkies was first to find an infinite series of solutions to Euler's equation with exactly one variable equal to zero, thus disproving Euler's sum of powers conjecture for the fourth power.



see also

Schoof

Schoof–Elkies–Atkin algorithm, extension of Schoof's algorithm by Noam Elkies and A. O. L. Atkin to improve its efficiency