國家理論科學研究中心學術演講
 NCTS Number Theory Seminar

Speaker:       Professor Matt A. Papanikolas (Texas A&M University)

Time     :       July 21 (Wednesday) PM 2:00

Topic    :       Carlitz logarithms and transcendence

Abstract:

    The Carlitz exponential function plays many of the roles over global function fields that the usual exponential function does over number fields. For example, its division values provide the basis for an explicit class field theory for F_q(T). Also, it is the uniformizing exponential function for the primary example of a Drinfeld module, the Carlitz module.

    In 1997, J. Yu proved the analogue for Carlitz logarithms of A. Baker's celebrated result on linear forms in logarithms. In this talk we will present new results on the algebraic independence of Carlitz logarithms. In particular, by utilizing a Tannakian formalism for Drinfeld modules, we prove that Carlitz logarithms that are linearly independent over F_q(T) are in fact algebraically independent.

Place     :

Lecture Room B,

National Center for Theoretical Sciences

4th Floor, The 3rd General Building,

National TsingHua University