Metric theorems on the estimation of integrals by sums
On the decomposition of vectors over number fields.
The number of irreducible factors of a polynomial, II
Heights, regulators and Schinzel's determinant inequality
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.
A Banach space determined by the Weil height
Page 1