Courses / Activities

Periods and logarithms of Drinfeld modules

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Matt Papanikolas

2009-05-21
09:00:00 - 09:50:00

Periods and logarithms of Drinfeld modules

101 , Mathematics Research Center Building (ori. New Math. Bldg.)



Starting in the 1980's, Prof. Jing Yu demonstrated that the setting of Drinfeld modules provided ripe analogues over function fields of classical transcendence and algebraic independence results and conjectures for values of exponential functions of algebraic groups. In a series of breakthrough papers, Yu showed that periods and logarithms of Drinfeld modules t especially well into this framework, and he proved several linear independence results about them. By appealing to certain systems of Frobenius difference equations, we find that periods and logarithms also arise as values of special entire functions and that algebraic relations among them are related to their associated Galois group. Using calculations with these Galois groups, we prove new algebraic independence results on periods and logarithms. Joint work with Chieh-Yu Chang.