Minima of Epstein’s Zeta function and heights of flat tori

By Peter Sarnak, Andreas Strombergsson. 2006

141 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a38830953890c5f8d91178fc5567018049570faf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Salvatore Torquato
2. Mathieu Lewin
3. Xavier Blanc

In Geometry and Topology

1. Salvatore Torquato
2. Mathieu Lewin
3. Xavier Blanc

Citations in the corpus

• Hyperuniformity in point patterns and two-phase random heterogeneous media (2009, background): “It is known that in two dimensions the triangular lattice minimizes the Epstein zeta function [34]–[37], [32] among all lattices; in three dimensions the FCC is at least a local minimum among lattices [38, 32], and for dimensions 4, 8, and 24 the densest known lattice packings are local minima [32].”
• Hyperuniform states of matter (2018, background): “Sarnak and Strömbergsson [150] proved that for dimensions 4, 8, and 24, the densest known lattice packings (checkerboard lattice D4, E8 root lattice and Leech lattice L24) are at least local minima.”
• The Crystallization Conjecture: A Review (2015, methodology): “In a famous article [218], Sarnak and Strömbergsson determined special local minima in dimensions 4, 8 and 24 (see also [58, 62, 63]).”