Über die Diskrepanz von Folgen in bewerteten Körpern

Abstract

Let k be a field which is locally compact with respect to a valuation ||, let X denote the subset X={α ∈ k, |α|≤1}. This paper is concerned with sequences of elements of X with respect to the theory of uniform distribution. Let D_N(ω) denote the discrepancy of the sequence ω=(x_n). It is proved that for archimedian valuations

with a certain constant

for every sequence ω. In the non-archimedian case there exist sequences ω with$D_N (\omega ) = \frac{1}{N}.$.