A motivic pairing and the Mellin transform in function fields

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-01 DOI:10.1016/j.aim.2024.109962

Nathan Green

引用次数: 0

Abstract

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 these pairings 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 transform 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.

查看原文本刊更多论文

函数场中的动机配对和梅林变换

我们定义了两种配对关系，它们分别涉及无性安德森 A 模块的 A 动量和对偶 A 动量。我们证明这些配对的特殊化给出了这个安德森 A 模块的指数函数和对数函数，并利用这些特殊化给出了指数函数和对数函数系数的精确公式。然后，我们利用这些配对将指数函数和对数函数表示为某些无穷积的求值。作为这些思想的应用，我们证明了黎曼zeta函数在卡利茨zeta值情况下的梅林变换公式。我们还举例说明了我们的结果如何适用于卡利茨多重zeta值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.