311 citations · 1.2k across the 55 of their papers we have counts for
36 papers · 1 filter
An elliptic K3 surface X/Q(t) with Mordell-Weil rank 17, I: Formulas for X and base changes of rank 18 and 19
Noam D. Elkies
In [Elkies 2006, Elkies 2007] we announced a K3 surface X/Q with Néron--Severi group NS(X) = NS_Q(X) of rank 19 and an elliptic fibration of Mordell--Weil rank 17. This is the larg…
Fast evaluation of Riemann theta functions in any dimension
Noam D. Elkies, Jean Kieffer
We describe an algorithm to numerically evaluate Riemann theta functions in any dimension in quasi-linear time in terms of the required precision, uniformly on reduced input. This…
The constructive inverse Galois problem via Hilbert modular forms: realizing the transitive group 17T7
Raymond van Bommel, Edgar Costa, Noam D. Elkies +3
We show how Hilbert modular forms can be used in the constructive inverse Galois problem over the rationals. In particular, we prove that the transitive permutation group 17T7, iso…
New Rank Records For Elliptic Curves Having Rational Torsion
Noam D. Elkies, Zev Klagsbrun
We present rank-record breaking elliptic curves having torsion subgroups Z/2Z, Z/3Z, Z/4Z, Z/6Z, and Z/7Z.
Periodic continued fractions over -integers in number fields and Skolem's -adic method
Bradley W. Brock, Noam D. Elkies, Bruce W. Jordan
We generalize the classical theory of periodic continued fractions (PCFs) over to rings of -integers in a number field. Let ${\mathcal B}=\{β, {β^*}…
The average size of the 3-isogeny Selmer groups of elliptic curves
Manjul Bhargava, Noam Elkies, Ari Shnidman
The elliptic curve admits a natural 3-isogeny . We compute the average size of the -Selmer group as varies over the…