On the non-critical exceptional zeros of Katz $p$-adic $L$-functions for CM fields

Abstract

The primary goal of this article is to study $p$-adic Beilinson conjectures in the presence of exceptional zeros for Artin motives over CM fields. In more precise terms, we address a question raised by Hida and Tilouine on the order of vanishing of Katz $p$-adic $L$-functions associated to CM fields, by means of a leading term formula we prove in terms of Rubin-Stark elements. In the particular case when the CM field in question is imaginary quadratic, our leading term formula and its consequences we record herein are unconditional.

arXiv comment39 pages. Final version, to appear in Advances in Mathematics (may differ from the journal version)

Cited by in corpus (2)

• The derivative formula of $p$-adic $L$-functions for imaginary quadratic fields at trivial zeros
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