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arXiv · 2409.08417

Lower order terms in the shape of cubic fields

Robert Hough·Eun Hye Lee
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Abstract

We demonstrate equidistribution of the lattice shape of cubic fields when ordered by discriminant, giving an estimate in the Eisenstein series spectrum with a lower order main term. The analysis gives a separate discussion of the contributions of reducible and irreducible binary cubic forms, following a method of Shintani. Our work answers a question posed at the American Institute of Math by giving a precise geometric and spectral description of an evident barrier to equidistribution in the lattice shape.

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Robert Hough, Eun Hye Lee. 2024-09-12. Lower order terms in the shape of cubic fields. https://arxiv.org/abs/2409.08417

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