Brownawell and Denis constructed, as extensions of Drinfeld modules by additive groups, a t-module whose periods can be expressed in terms of hyperderivatives of the periods and quasi-periods of the given Drinfeld module. In this talk, we discuss how to obtain hyperderivatives of periods, quasi-periods, logarithms and quasi-logarithms of an abelian, A-finite, and uniformizable t-module in terms of the rigid analytic trivialization of an abelian, A-finite, and uniformizable t-module. In the process, we determine explicit descriptions of periods, quasi-periods, logarithms, and quasi-logarithms in terms of a rigid analytic trivializations. In particular, we prove that non-tractable coordinates of periods and logarithms of uniformizable, abelian, and A-finite t-modules can be explicitly related to tractable coordinates of periods and logarithms of Maurischat’s prolongation of the t-module. This is joint work with Matt Papanikolas.

 

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