On the order of vanishing of Stickelberger elements of Hilbert modular forms

Abstract

We construct Stickelberger elements for Hilbert modular cusp forms of parallel weight 2 and use recent results of Dasgupta and Spieß to bound their order of vanishing from below. As a special case the vanishing part of Mazur and Tate's refined 'Birch and Swinnerton-Dyer type'-conjecture for elliptic curves of rank 0 follows.