论文标题
$ P $ -ADIC $ l $ f $ for timinary Quadratic字段的衍生式公式
The derivative formula of $p$-adic $L$-functions for imaginary quadratic fields at trivial zeros
论文作者
论文摘要
Hilbert Modular形式之间的一致性在Darmon-Dasgupta-Pollack和Ventullo的作品中解决了DeLigne-Im-ribet $ P $ -ADIC $ L $ functions的列为一定的猜想。本文的目的是通过CM表格和非CM表单之间的一致性证明对假想二次界面附带的Katz $ P $ -ADIC $ L $ functions的总体猜想的类似物。新的成分是应用$ p $ -ADIC RANKIN-SELBERG方法来构建一个非CM HIDA家族，该家族与$ 1+\ varepsilon $ pecialization的HIDA CM家族一致。
The rank one Gross conjecture for Deligne-Ribet $p$-adic $L$-functions was solved in works of Darmon-Dasgupta-Pollack and Ventullo by the Eisenstein congruence among Hilbert modular forms. The purpose of this paper is to prove an analogue of the Gross conjecture for the Katz $p$-adic $L$-functions attached to imaginary quadratic fields via the congruences between CM forms and non-CM forms. The new ingredient is to apply the $p$-adic Rankin-Selberg method to construct a non-CM Hida family which is congruent to a Hida family of CM forms at the $1+\varepsilon$ specialization.
