Algebraic proof of modular form inequalities for optimal sphere packings
Seewoo Lee
TL;DR
This paper provides algebraic proofs for modular form inequalities that underpin the optimal sphere packings in 8 and 24 dimensions, confirming their mathematical bounds.
Contribution
It introduces algebraic proof techniques for existing modular form inequalities related to sphere packings in high dimensions.
Findings
Confirmed the inequalities for 8 and 24-dimensional packings.
Provided algebraic proofs as an alternative to previous methods.
Strengthened the mathematical foundation of optimal sphere packings.
Abstract
We give algebraic proofs of Viazovska and Cohn-Kumar-Miller-Radchenko-Viazovska's modular form inequalities for 8 and 24-dimensional optimal sphere packings.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.