Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant

Abstract

Explicit upper bounds are developed for the class number and the regulator of any cubic field with a negative discriminant. Lower bounds on the class number are also developed for certain special pure cubic fields.

Stable parallelizability of partially oriented flag manifolds

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𝐿-functions and class numbers of imaginary quadratic fields and of quadratic extensions of an imaginary quadratic field

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