2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63194We formulate several variants of a conjecture relating the arithmetic degree of certain hermitian fibre bundles with the values of the logarithmic derivative of Artin's L-functions at negative integers. This generalizes conjectures by Colmez and Gross-Deligne and complements Beilinson's conjectures for the Artin motives. We announce several results in the direction of these statements.AMS-LaTeX, 8 pages, submittedAlgebraic GeometryNumber Theory11G18; 11G40; 11G50; 14G35; 14G40text