311 citations · 1.2k across the 55 of their papers we have counts for
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Equations for a K3 Lehmer map
Simon Brandhorst, Noam D. Elkies
McMullen proved that there exists an automorphism of minimal topological entropy on a projective K3 surface. We derive equations for the surface and its automorphism. We reconstruc…
Genus 1 fibrations on the supersingular K3 surface in characteristic 2 with Artin invariant 1
Noam D. Elkies, Matthias Schuett
The supersingular K3 surface X in characteristic 2 with Artin invariant 1 admits several genus 1 fibrations (elliptic and quasi-elliptic). We use a bijection between fibrations and…
Modular forms and K3 surfaces
Noam D. Elkies, Matthias Schuett
For every known Hecke eigenform of weight 3 with rational eigenvalues we exhibit a K3 surface over QQ associated to the form. This answers a question asked independently by Mazur a…
Points of Low Height on Elliptic Curves and Surfaces, I: Elliptic surfaces over P^1 with small d
Noam D. Elkies
For each of n=1,2,3 we find the minimal height h^(P) of a nontorsion point P of an elliptic curve E over C(T) of discriminant degree d=12n (equivalently, of arithmetic genus n), an…
Curves of every genus with many points, II: Asymptotically good families
Noam D. Elkies, Everett W. Howe, Andrew Kresch +3
We resolve a 1983 question of Serre by constructing curves with many points of every genus over every finite field. More precisely, we show that for every prime power q there is a…
The identification of three moduli spaces
Noam D. Elkies
It is one of the wonderful ``coincidences'' of the theory of finite groups that the simple group G of order 25920 arises as both a symplectic group in characteristic 3 and a unitar…