Inequalities involving polynomials and quasimodular forms
Abstract
In this paper, we study inequalities involving polynomials and quasimodular forms. More precisely, we focus on the monotonicity of the functions of the form $t \mapsto t^m F(it)$ where $F$ is a quasimodular form and $m > 0$. As an application, we construct infinitely many positive quasimodular forms of level $> 1$. We also give alternative proofs of modular form inequalities used in the proof of optimality of Leech lattice packing and universal optimality of the lattice by Cohn, Kumar, Miller, Radchenko, and Viazovska.
Fields of Study & Subjects
Advanced Mathematical Identities
Analytic Number Theory Research
Advanced Algebra and Geometry
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 11 February 2026
- Language
- EN
- Document type
- Preprint