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math.NT2025
Disproving the quasi-uniformity of the Halton sequences and of some Halton-type sequences
Takashi Goda, Roswitha Hofer, Kosuke Suzuki
In this short article, we prove that the Halton sequence, one of the most well-known low-discrepancy sequences, is not quasi-uniform in any dimension with any pairwise re…
math.NT2025
Variants of the Littlewood conjecture, their connection to uniformly distributed sequences, and the exact order of the discrepancy of van der Corput--Kronecker-type sequences
Roswitha Hofer
The aims of this paper are twofold. First, it discusses the Littlewood conjecture and its variants with respect to uniformly distributed sequences. The second aim is to determine t…