Photo from archive.org
We generalize the recent work of Viazovska by constructing infinite families of Schwartz functions, suitable for Cohn–Elkies style linear programming bounds, using quasi-modular and modular forms. In particular, for dimensions… Click to show full abstract
We generalize the recent work of Viazovska by constructing infinite families of Schwartz functions, suitable for Cohn–Elkies style linear programming bounds, using quasi-modular and modular forms. In particular, for dimensions $$d \equiv 0 \pmod {8}$$ d ≡ 0 ( mod 8 ) , we give new constructions for obtaining sphere packing upper bounds via modular forms. In dimension 8 and 24, these exactly match the functions constructed by Viazovska and Cohn, Kumar, Miller, Radchenko, and Viazovska which resolved the sphere packing problem in those dimensions.
Journal Title: Archiv der Mathematik
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!