论文标题
动机配对和功能领域中的梅林变换
A Motivic Pairing and the Mellin Transform in Function Fields
论文作者
论文摘要
我们定义了两个与Abelian Anderson A模块的双重A-Motive相关的配对。我们表明，这些配对的专业化为Anderson A模块的指数和对数函数提供了指数和对数函数，并且我们使用这些专业知识为指数和对数函数的系数提供精确的公式。然后，我们使用此配对来表达指数和对数功能作为对某些无限产物的评估。作为这些想法的应用，我们证明了在Carlitz Zeta值的情况下，Riemann Zeta功能的Mellin Tranform公式的类似物。我们还举例说明了我们的结果如何适用于carlitz多个Zeta值。
We define two pairings relating the A-motive with the dual A-motive of an abelian Anderson A-module. We show that specializations of these pairings give the exponential and logarithm functions of this Anderson A-module, and we use these specializations to give precise formulas for the coefficients of the exponential and logarithm functions. We then use this pairing to express the exponential and logarithm functions as evaluations of certain infinite products. As an application of these ideas, we prove an analogue of the Mellin tranform formula for the Riemann zeta function in the case of Carlitz zeta values. We also give an example showing how our results apply to Carlitz multiple zeta values.
