2022/05/12 by Nathan Green, Green, Nathan
Mathematics · #11G09 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2205.06120
openalex publication_date 2022/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.