Mathematics Senior Capstone Papers
Document Type
Article
Publication Date
Spring 2023
Abstract
Drinfeld modules are, in essence, a way to create a function field analogue to complex multiplication. With these modules, we can define a logarithm function analogous to the natural logarithm by virtue of a power series. Similarly to how we extend the radius of convergence of the natural logarithm with complex numbers, we can also extend the radius of convergence for these Drinfeld module logarithms. While there are proofs for extending the radius of convergence of the Carlitz module, the simplest form of Drinfeld module, there is no proof for a generalized Drinfeld. In this paper, a method of extending the Carlitz logarithm’s radius of convergence using Newton polygons will be examined. Afterwards, a way to apply this proof to a general Drinfeld logarithm function will be walked through.
Recommended Citation
Clapp, Ethan, "Extending the Radius of Convergence of the Drinfeld Module Logarithm" (2023). Mathematics Senior Capstone Papers. 32.
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/32