The distribution of Galois orbits of low height

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Date

2003

Authors

Petsche, Clayton Jay

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Abstract

We establish quantitative estimates on the complex distribution of Gal(Q¯ /Q) orbits of low height. In particular, we consider a family of heights hs : Q¯ → [0, +∞), including the usual logarithmic absolute Weil height h0, in which the Ls-norm is used at the archimedean places. We then give a variety of Koksma-type inequalities, realizing the heights hs as a family of discrepancies on Galois orbits in Q¯ . As an application, we give quantitative versions of Langevin’s lower bound on hs.

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