论文标题
CM的一致性和Katz $ P $ -ADIC $ L $ f $ for CM字段的零件
CM congruence and trivial zeros of the Katz $p$-adic $L$-functions for CM fields
论文作者
论文摘要
本文的目的是调查CM一致性的Katz $ P $ -ADIC $ L $ functions的微不足道的零。我们证明存在Katz $ P $ -ADIC $ L $ l $ functions的琐碎零，并在琐事零下建立了Cycotomic $ p $ p $ p $ p $ p $ p $ p $ p $ l $ incortions的第一个衍生公式。我们证明的关键成分是CM田地的特殊情况，包括$ p $ -ADIC KRONECKER限制公式，以及通过CM和非CM HIDA HIDA HIDA家族之间的明确零零零的反合式$ p $ p $ p $ p $ p $ $ p $ p $ p $ l $ l $ functions的术语公式。
The aim of this paper is to investigate the trivial zeros of the Katz $p$-adic $L$-functions by the CM congruence. We prove the existence of trivial zeros of the Katz $p$-adic $L$-functions for general CM fields and establish a first derivative formula of the cyclotomic $p$-adic $L$-functions at trivial zeros under some Leopoldt hypothesis. The crucial ingredients in our proof are a special case of $p$-adic Kronecker limit formula for CM fields and a leading term formula of anticyclotomic $p$-adic $L$-functions at trivial zeros via the explicit congruences between CM and non-CM Hida families of Hilbert cusp forms.
