Algebra Seminar: Logarithmic Derivatives in function fields -- William Cherry | Department of Mathematics

Algebra Seminar: Logarithmic Derivatives in function fields -- William Cherry

Event Information
Event Location: 
GAB 473*
Event Date: 
Friday, October 7, 2016 - 2:00pm

(Note the time and room change.)

Abstract: Consider the field K of rational functions in one variable over
the complex numbers with its natural derivation. Let L be a finite field
extension of K with the derivation on K extended to L. Let f be an element
in L and f' its derivative. Can the field norm of f'/f be expressed as an
integral linear combination of logarithmic derivatives in K? I will discuss
some explicit calculations done by Cristina Toropu in the quadratic case
and some interpretations of them. I will then discuss the cubic case and
hope the audience can contribute some suggestions for how to approach the
general case.