On the number of perfect positive definite quadratic forms

Nikolay Moshchevitin

On the number of perfect positive definite quadratic forms

Number Theory 2026-07-05 v1

Authors: Nikolay Moshchevitin

Abstract

We prove a new asymptotic lower bound for the number of perfect positive definite quadratic forms in n variables which is close to the optimal one.

Keywords

perfect positive definite quadratic form asymptotic lower bound lattice

Cite

@article{arxiv.2607.04239,
  title  = {On the number of perfect positive definite quadratic forms},
  author = {Nikolay Moshchevitin},
  journal= {arXiv preprint arXiv:2607.04239},
  year   = {2026}
}

Comments

8 pages