2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184251Summations and relations involving the Hurwitz and Riemann zeta-functions are extended first to Barnes zeta-functions and then to zeta-functions of general type. The analysis is motivated by the evaluation of determinants on spheres which are treated both by a direct expansion method and by regularised sums. Comments on existing calculations are made. A Kaluza--Klein technique is introduced providing a determinant interpretation of the Glaisher-Kinkelin-Bendersky constants which are then generalised to arbitrary zeta-functions. This technique allows an improved treatment of sphere determinants.26 pages, JyTex. Minor improvements madeHigh Energy Physics - TheoryMathematical PhysicsClassical Analysis and ODEsSpectral Theorytext