On the Discrepancy of the Sequence (nα) Original Research Article

Let α be an irrational number and let D*N(α) denote the *-discrepancy of the sequence (nα)n ≥ 1 mod 1. We study the image of the map α maps to ν*(α) = imageN → ∞ND*N(α)/log N, one of the results being ν*(image\image) = [ν*(√2), ∞].