论文标题
Kubota-Leopoldt $ P $ -ADIC $ L $ functions的总和表达式
Sum Expressions for Kubota-Leopoldt $p$-adic $L$-functions
论文作者
论文摘要
当$ p $是一个奇怪的素数时，德尔伯戈观察到，当乘以辅助Euler因子时，任何kubota-leopoldt $ p $ p $ p $ p $ l $ unction都可以将其写成无限的总和。我们将通过计算适当措施的时期来建立此类表达式，而无需限制$ p $，而当角色不平凡时，我们将不限制Euler因素。作为一个应用程序，我们将为派生$ l_p'（0，χ）$的Ferrero-Greenberg公式拒绝Ferrero-Greenberg公式。我们还将根据基本$ p $ - adic分析及其与Stickelberger元素的关系讨论总和表达式的融合；此类讨论反过来提供了总和表达式的有效性的替代证明。
When $p$ is an odd prime, Delbourgo observed that any Kubota-Leopoldt $p$-adic $L$-function, when multiplied by an auxiliary Euler factor, can be written as an infinite sum. We shall establish such expressions without restriction on $p$, and without the Euler factor when the character is nontrivial, by computing the periods of appropriate measures. As an application, we will reprove the Ferrero-Greenberg formula for the derivative $L_p'(0,χ)$. We will also discuss the convergence of sum expressions in terms of elementary $p$-adic analysis, as well as their relation to Stickelberger elements; such discussions in turn give alternative proofs of the validity of sum expressions.
