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- W3196012927 abstract "We show that the shape of a complex cubic field lies on the geodesic of the modular surface defined by the field's trace-zero form. We also prove a general such statement for all orders in 'etale Q-algebras. Applying a method of Manjul Bhargava and Piper H to results of Bhargava and Ariel Shnidman, we prove that the shapes lying on a fixed geodesic become equidistributed with respect to the hyperbolic measure as the discriminant of the complex cubic field goes to infinity. We also show that the shape of a complex cubic field is a complete invariant (within the family of all cubic fields)." @default.
- W3196012927 created "2021-08-30" @default.
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- W3196012927 date "2021-06-30" @default.
- W3196012927 modified "2023-10-03" @default.
- W3196012927 title "Equidistribution of shapes of complex cubic fields of fixed quadratic resolvent" @default.
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- W3196012927 doi "https://doi.org/10.2140/ant.2021.15.1095" @default.
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