An improper Cramer-Rao lower bound

L. Gajek

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Lower Bounds on the Directed Sweepwidth of Planar Shapes

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Heights, regulators and Schinzel's determinant inequality

Shabnam Akhtari, Jeffrey D. Vaaler (2016)

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We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix proved by Schinzel. The lower bound for the S-regulator follows from Minkowski's theorem on successive minima and a volume formula proved by Meyer and Pajor. We establish similar upper bounds for the relative regulator of an extension l/k of number fields. ...