论文标题
$ \ MATHCAL {L} $ - 不变，$ P $ -Adic Heights和$ P $ -ADIC $ L $ functions的分解
$\mathcal{L}$-invariants, $p$-adic heights and factorization of $p$-adic $L$-functions
论文作者
论文摘要
我们继续研究Katz' $ p $ -adic $ l $ l $ functions to cm field $ k $的非关键特殊零，此后有两个线程。在第一个线程中，我们重新定义了（group-ring-valued）$ \ mathcal {l} $ - 与每个$ \ mathbb {z} _ {z} _ {p} $ - 扩展$k_γ$ $k_γ$ of $ p $ $ p $ - ad的高度配对，并插入$k_γ$ verivariate compliaive-k_γ$ - $ \ mathcal {l} $ - 不变。在第二个线程中，我们使用结果来研究非生殖器Rankin-selberg $ p $ -Adic $ l $ l $ functions，通过我们确定的因素化语句，与几乎普通CM家族的自我产生相关。分解定理是由于格林伯格和巴旺南引起的结果的扩展。
We continue with our study of the non-critical exceptional zeros of Katz' $p$-adic $L$-functions attached to a CM field $K$, following two threads. In the first thread, we redefine our (group-ring-valued) $\mathcal{L}$-invariant associated to each $\mathbb{Z}_{p}$-extension $K_Γ$ of $K$ in terms of $p$-adic height pairings and interpolate them as $K_Γ$ varies to a universal (multivariate) group-ring-valued $\mathcal{L}$-invariant. In the second thread, we use our results to study the exceptional zeros of the non-genuine Rankin--Selberg $p$-adic $L$-functions attached to the self-products of nearly ordinary CM families, via the factorization statements we establish. The factorization theorems are extensions of the results due to Greenberg and Palvannan.
