论文标题
A $ P $ -ADIC $ L $ - 函数，用于HIDA家庭的典型动机时期
A $p$-adic $L$-function with canonical motivic periods for Hida families
论文作者
论文摘要
2006年，福卡亚（Fukaya）和卡托（Kato）为大型动机制定了大约$ p $ - 亚种$ l $ functions，并从ETNC得出了精确的猜想插值公式。我们研究了HIDA家族中的这种猜想$ -ADIC $ L $ - 功能与Kitagawa构建的$ P $ -ADIC $ L $ - 功能相比。先验尚不清楚插值公式是否重合，主要是因为对时期（通过比较同构）的定义相当不明显，而这些定义出现在一般公式中。 使用$ p $ -ADIC EICHLER-SHIMURA同构及其在HIDA家族中的插值，我们将这些时期与Kitagawa公式中的表达式进行了比较。在某些情况下，这可以修改Kitagawa的构造，从而产生与福卡亚和加藤的猜想兼容的$ P $ adic $ l $ lunction。
In 2006, Fukaya and Kato formulated a general conjecture about $p$-adic $L$-functions for a large class of motives and derived a precise conjectural interpolation formula from the ETNC. We study this conjectural $p$-adic $L$-function in the setting of Hida families and compare it to the $p$-adic $L$-function constructed by Kitagawa. A priori it is not clear whether the interpolation formulas coincide, mainly because of the rather inexplicit definition of periods (via comparison isomorphisms) that appear in the general formula. Using $p$-adic Eichler-Shimura isomorphisms and their interpolation in Hida families, we compare these periods to the expressions in Kitagawa's formula coming from modular symbols. This allows in certain cases to modify Kitagawa's construction such that it produces a $p$-adic $L$-function compatible with Fukaya's and Kato's conjecture.
