2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111552We obtain a series improvement to higher-order $L^p$-Rellich inequalities on a Riemannian manifold $M$. The improvement is shown to be sharp as each new term of the series is added.Slightly revised. To appear in Math. Z. 19 pagesAnalysis of PDEsSpectral Theory35J35; 35P15; 26D10Best constants for higher-order Rellich inequalities in $L^p(Ω)$text