论文标题
关于正规化的伯努利分布和p-adic dirichlet扩展的注释
A note on regularized Bernoulli distributions and p-adic Dirichlet expansions
论文作者
论文摘要
我们考虑Bernoulli发行版及其正常化，这是$ p $ - adiC Integers $ \ mathbb {z} _p $的措施。众所周知，他们的梅林变换可用于定义$ p $ - adic $ l $ functions。我们表明，对于$ p> 2 $，一个正规化的bernoulli发行版之一特别简单，等于$ \ mathbb {z} _p $，该度量$ \ pm \ pm \ pm \ frac {1} {1} {2} {2} $ clopen球上的$。我们将其应用于$ p $ - 功率导体的Dirichlet字符的$ P $ -ADIC $ L $ functions，并获得类似于复杂情况的Dirichlet系列扩展。 D. Delbourgo研究了此类扩展，此贡献通过$ p $ -Adic措施提供了一种方法。
We consider Bernoulli distributions and their regularizations, which are measures on the $p$-adic integers $\mathbb{Z}_p$. It is well known that their Mellin transform can be used to define $p$-adic $L$-functions. We show that for $p>2$ one of the regularized Bernoulli distributions is particularly simple and equal to a measure on $\mathbb{Z}_p$ that takes the values $\pm \frac{1}{2}$ on clopen balls. We apply this to $p$-adic $L$-functions for Dirichlet characters of $p$-power conductor and obtain Dirichlet series expansions similar to the complex case. Such expansions were studied by D. Delbourgo, and this contribution provides an approach via $p$-adic measures.
