多切函数代数

摘要：

多值是出现在许多不同上下文中的数字。不幸的是，他们的算法仍然遥不可及。在这篇文章中，我们定义了一个功能模拟的代数的multizeta值，即代数的multitangent功能，这是1-周期函数定义的过程形式上类似于multizeta值。我们在这里介绍的基本概念，减少到单调的功能，投影到multitangent功能和三因子分解，给出了一种方式来写一个multitangent功能的Hurwitz multitzeta功能。这就解释了为什么多切代数是多zeta值代数的一个功能类似物。然后，我们讨论了最重要的代数和分析性质的这些功能和后果的multizeta值，以及他们的正规化的发散情况下。多切线的每个属性在多zeta值的一侧都有一个挂件。这使我们能够提出新的结构，这些结构已经被检查到18的重量。

英文摘要：

Multizeta values are numbers appearing in many different contexts. Unfortunately, their arithmetics remains mostly out of reach. In this article, we define a functional analogue of the algebra of multizetas values, namely the algebra of multitangent functions, which are 1- periodic functions defined by a process formally similar to multizeta values. We introduce here the fundamental notions of reduction into monotangent functions, projection onto multitangent functions and that of trifactorization, giving a way of writing a multitangent function in terms of Hurwitz multizeta functions. This explains why the multitangent algebra is a functional analogue of the algebra of multizeta values. We then discuss the most important algebraic and analytic properties of these functions and their consequences on multizeta values, as well as their regularization in the divergent case. Each property of multitangents has a pendant on the side of multizeta values. This allows us to propose new conjectures, which have been checked up to the weight 18.

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