Robert Hough, Eun Hye Lee
Published 2024-09-12Version 1
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.
Comments: Preliminary version. arXiv admin note: substantial text overlap with arXiv:2007.03170
Lower order terms for the one-level densities of symmetric power $L$-functions in the level aspect
Lower order terms for the moments of symplectic and orthogonal families of $L$-functions
Secondary terms in counting functions for cubic fields
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