2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62608The asymptotic trace formula of A. Connes is restated in a semi-local form, thus showing that the difficulties in giving a direct proof do not lie in the change of topology when transgressing from finitely many places to infinitely many.LATEX 19 pagesNumber TheoryA semi-local trace identity and the Riemann hypothesis for function fieldstext