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arXiv · 1901.04807

An upper bound on the number of perfect quadratic forms

Wessel P. J. van Woerden
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Abstract

In a recent preprint on arXiv Roland Bacher showed that the number $p_d$ of non-similar perfect $d$-dimensional quadratic forms satisfies $e^{\Omega(d)} < p_d < e^{O(d^3\log(d))}$. We improve the upper bound to $e^{O(d^2\log(d))}$ by a volumetric argument based on Voronoi's first reduction theory.

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Wessel P. J. van Woerden. 2019-01-15. An upper bound on the number of perfect quadratic forms. https://doi.org/10.1016/j.aim.2020.107031

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