The true order of magnitude of Lame rounding error sums

摘要

Let Ψ(z) := z-[z]-1/2 (z ∈ R). Further let λ denote a large real parameter. We show that for arbitrary real numbers k and αwith k ≧ 2.7013 and 0 < α ≦ 1. Σ from 0 ≦ n ≦ αλ of ((λ~k-n~k)~(1/k)) = {0 Ω_±}(λ~(1-1/k)) (λ → ∞).