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A $p$-adic Gross-Zagier formula for twisted triple product $p$-adic $L$-functions attached to finite slope families

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arxiv 2501.17474 v1 pith:VJP2225I submitted 2025-01-29 math.NT math.AG

Ting-Han Huang , Ananyo Kazi This is my paper · ORCID
classification math.NTmath.AG
keywords adicfamiliesfiniteformulagross-zagiermainproductslope
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abstract

Our main objective in the present paper is to generalise the work of Blanco-Chac\'{o}n and Fornea on the $p$-adic Gross-Zagier formula for twisted triple product $p$-aidc $L$-function. We extend their main result to the case of finite slope families of Hilbert modular forms and also allow the prime $p$ to be inert in the real quadratic field $L$.

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  1. New perspectives on $p$-adic regulator formulae

    math.NT 2026-01 conditional novelty 6.0 of 10

    A finite-slope p-adic regulator formula for Asai–Flach classes is proved without finite-polynomial cohomology, and diagonal classes are reconstructed as pullback extension classes.

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