Effective rigid analytic trivializations for Drinfeld modules Academic Article

abstract

• AbstractWe develop tools for constructing rigid analytic trivializations for Drinfeld modules as infinite products of Frobenius twists of matrices, from which we recover the rigid analytic trivialization given by Pellarin in terms of Anderson generating functions. One advantage is that these infinite products can be obtained from only a finite amount of initial calculation, and consequently we obtain new formulas for periods and quasi-periods, similar to the product expansion of the Carlitz period. We further link to results of Gekeler and Maurischat on the $infty $ -adic field generated by the period lattice.

authors

• Papanikolas, Matthew

published proceedings

• CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES

author list (cited authors)

• Khaochim, C., & Papanikolas, M. A.

citation count

• 0

complete list of authors

• Khaochim, Chalinee||Papanikolas, Matthew A

publication date

• June 2023

publisher

• Canadian Mathematical Society  Publisher

published in

• Canadian Journal of Mathematics  Journal

keywords

• Anderson Generating Functions
• Drinfeld Modules
• Infinite Product Expansions
• Periods
• Quasi-periods
• Rigid Analytic Trivializations
• T-division Sequences

Digital Object Identifier (DOI)

• 10.4153/S0008414X22000153

start page

• 713

end page

• 742

volume

• 75

issue

• 3

URL

• http://dx.doi.org/10.4153/s0008414x22000153