Leading terms of anticyclotomic Stickelberger elements and p-adic periods

Abstract

Let E be a quadratic extension of a totally real number field. We construct Stickelberger elements for Hilbert modular forms of parallel weight 2 in anticyclotomic extensions of E. Extending methods developed by Dasgupta and Spieß from the multiplicative group to an arbitrary one-dimensional torus we bound the order of vanishing of these Stickelberger elements from below and, in the analytic rank zero situation, we give a description of their leading terms via automorphic L-invariants. If the field E is totally imaginary, we use the p-adic uniformization of Shimura curves to show the equality between automorphic and arithmetic L-invariants. This generalizes a result of Bertolini and Darmon from the case that the ground field is the field of rationals to arbitrary totally real number fields.

30 pages, minor changes

References in corpus (2)

• Darmon points on elliptic curves over number fields of arbitrary signature
• On the order of vanishing of Stickelberger elements of Hilbert modular forms

Cited by in corpus (1)

• The universal $p$-adic Gross-Zagier formula