Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on special values of positive characteristic L-series and in transcendence and algebraic independence problems. In the present paper we investigate techniques for expressing Anderson generating functions in terms of the defining polynomial of the Drinfeld module and determine new formulas for periods and quasi-periods.
We provide explicit series expansions for the exponential and logarithm
functions attached to a rank r Drinfeld module that generalize well known
formulas for the Carlitz exponential and logarithm. Using these results we
obtain a procedure and an analytic expression for computing the periods of rank
2 Drinfeld modules and also a criterion for supersingularity.Comment: 20 page
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