The Algebra of Multitangent Functions
The Algebra of Multitangent Functions
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多重切函数的代数
DOI：
10.1016/j.jalgebra.2013.12.016
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Olivier Bouillot
中科院分区：
文献类型：
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作者：
Olivier Bouillot
多值是出现在许多不同上下文中的数字。在这篇文章中，我们定义了一个多zeta值代数的函数类似物，即多正切函数代数，它是由形式上类似于多zeta值的过程定义的1-周期函数。我们在这里介绍了单调函数化约，多正切函数投影和三因子分解的基本概念，给出了用Hurwitz多重zeta函数表示多重正切函数的方法。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。然后我们讨论了这些函数最重要的代数和解析性质及其对multizeta值的影响，以及它们在发散情况下的正则化。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。
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 multizeta 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.