Let \(\textit{K}\) be a cubic number field. In this paper, we study the Ramanujan sums \(c_{\mathcal {J}}(\mathcal {I})\), where \(\mathcal {I}\) and {J}\) are integral ideals in {O}_\textit{K}\). The asymptotic behaviour of {I})\) over both is investigated.

HIPPARCOS satellite parallaxes for 22 metal-poor field horizontal branch stars with V0 < 9 are used to derive their absolute magnitude. The weighted mean value is MV = +0.69± 0.10 for an average metallicity of [Fe/H]=−1.41; a somewhat brighter average magnitude of MV = +0.60± 0.12 for an average metallicity of [Fe/H]=−1.51 is obtained eliminating HD17072, that might be on the first ascent of th...