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math.NT2026
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…
math.NT2026
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…
math.NT2025
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…