Annihilating class groups in p-elementary abelian extensions

Abstract We derive new cases of conjectures of Rubin and of Burns–Kurihara–Sano concerning derivatives of Dirichlet L -series at $s = 0$ in p -elementary abelian extensions of number fields for arbitrary prime numbers p . In naturally arising examples of such extensions one therefore obtains annihilators of class groups from S -truncated Dirichlet L -series for ‘large-enough’ sets of places S .