Triple product $p$-adic $L$-functions for finite slope families and a $p$-adic Gross-Zagier formula

Ting-Han Huang

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arXiv · 2403.18620

Triple product $p$-adic $L$-functions for finite slope families and a $p$-adic Gross-Zagier formula

Ting-Han Huang

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Abstract

In this paper, we generalize two results of H. Darmon and V. Rotger on triple product $p$-adic $L$-functions associated with Hida families to finite slope families. We first prove a $p$-adic Gross-Zagier formula, then demonstrate an application to a special case of the equivariant Birch and Swinnerton-Dyer conjecture for supersingular elliptic curves.

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Ting-Han Huang. 2024-03-27. Triple product $p$-adic $L$-functions for finite slope families and a $p$-adic Gross-Zagier formula. https://arxiv.org/abs/2403.18620

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