• Corpus ID: 248721980

A Motivic Pairing and the Mellin Transform in Function Fields

```@inproceedings{Green2022AMP,
title={A Motivic Pairing and the Mellin Transform in Function Fields},
author={Nathan Green},
year={2022}
}```
. 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…

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Appendix. the Mellin Transform and Related Analytic Techniques

1. The generalized Mellin transformation The Mellin transformation is a basic tool for analyzing the behavior of many important functions in mathematics and mathematical physics, such as the zeta