Hyperderivatives of periods and quasi-periods of t-modules


Matt Papanikolas ( Texas A&M University, USA )
2018-06-08  10:30 - 11:30
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

Brownawell and Denis have defined divided derivatives of a Drinfeld module, which are Anderson t-modules that are iterated extensions of the Drinfeld module by the additive group. They showed that the periods of the divided derivative of the Drinfeld module are explicitly expressible in terms of the hyperderivatives of the periods and quasi-periods of the Drinfeld module itself. One question that arises from this theory is to what extent are these quantities and objects related to solutions of Frobenius semilinear difference equations associated to (abelian) Anderson t-modules? In this talk we will discuss how to realize hyperderivatives of periods and quasi-periods of an abelian Anderson t-module as themselves periods and quasi-periods of Maurischat\'s prolongation t-modules of the given t-module. As part of this investigation we determine also the general theory of realizing periods, quasi-periods, logarithms, and quasi-logarithms of abelian Anderson t-modules through solutions of Frobenius semilinear equations, by building on the theory of Anderson for periods and logarithms and using Anderson generating functions together with results of Hartl and Juschka to account for quasi-periods and quasi-logarithms. Joint with C. Namoijam.