The distribution of Galois orbits of low height
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.