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.

28 pages, typos corrected, small changes in Section 2.3

References in corpus (1)

• The Eisenstein cocycle, partial zeta values and Gross--Stark units

Cited by in corpus (4)

• Leading terms of anticyclotomic Stickelberger elements and p-adic periods
• Anticyclotomic p-adic l-functions and the exceptional zero phenomenon
• Kato's Euler system and the Mazur-Tate refined conjecture of BSD type
• Eichler-Shimura isomorphism and group cohomology on arithmetic groups