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

Kazim Buyukboduk; Ryotaro Sakamoto

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

Number Theory 2022-05-11 v2

Authors: Kazim Buyukboduk , Ryotaro Sakamoto

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.

Keywords

p-adic l-functions cm fields exceptional zeros beilinson conjectures rubin-stark elements artin motives

Cite

@article{arxiv.1904.01644,
  title  = {On the non-critical exceptional zeros of Katz $p$-adic $L$-functions for CM fields},
  author = {Kazim Buyukboduk and Ryotaro Sakamoto},
  journal= {arXiv preprint arXiv:1904.01644},
  year   = {2022}
}

Comments

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

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

Abstract

Keywords

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