Hyperderivatives of periods and quasi-periods for Anderson $t$-modules Academic Article uri icon

abstract

  • We investigate periods, quasi-periods, logarithms, and quasi-logarithms of Anderson $t$-modules, as well as their hyperderivatives. We develop a comprehensive account of how these values can be obtained through rigid analytic trivializations of abelian and $mathbf{A}$-finite $t$-modules. To do this we build on the exponentiation theorem of Anderson and investigate quasi-periodic extensions of $t$-modules through Anderson generating functions. By applying these results to prolongation $t$-modules of Maurischat, we integrate hyperderivatives of these values together with previous work of Brownawell and Denis in this framework.

author list (cited authors)

  • Namoijam, C., & Papanikolas, M. A.

publication date

  • January 1, 2021 11:11 AM