Hyperderivatives of periods and quasi-periods for Anderson $t$-modules

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.

111 pages

References in corpus (2)

• Algebraic independence of the Carlitz period and its hyperderivatives
• Algebraic relations among hyperderivatives of periods and logarithms of Drinfeld modules

Cited by in corpus (5)

• Effective rigid analytic trivializations for Drinfeld modules
• Algebraic relations among hyperderivatives of periods and logarithms of Drinfeld modules
• Linear equations on Drinfeld modules
• Linear relations among algebraic points on tensor powers of the Carlitz module
• Abelian equals A-finite for Anderson A-modules