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arXiv · 1607.01197

Leading terms of anticyclotomic Stickelberger elements and p-adic periods

Felix Bergunde·Lennart Gehrmann
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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 Spie{\ss} 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.

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Felix Bergunde, Lennart Gehrmann. 2016-07-05. Leading terms of anticyclotomic Stickelberger elements and p-adic periods. https://doi.org/10.1090/tran/7120

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