Hauptseminar Analytische Zahlentheorie und Diophantische Approximation
Dozent:innen: Jun. Prof. Dr. Ariyan Javan PeykarKurzname: ZTH-001
Kurs-Nr.: 08.105.141
Kurstyp: Hauptseminar
Voraussetzungen / Organisatorisches
Die Anmeldung erfolgt nicht über Jostustine, sondern wird Anfang des Sommersemesters durch das Studienbüro vorgenommen.Inhalt
A complex number x is an algebraic number if there is a non-constant polynomial f with rational coefficients such that f(x) =0.A non-algebraic complex number is called a transcendental number.
One of the first things we will prove in this seminar is the classical theorem of Lindemann-Weierstrass.
This beautiful theorem implies the transcendence of pi, exp(1), and many more real numbers appearing in "nature".
We also investigate the finiteness (or non-finiteness) or certain Diophantine equations. This naturally leads to studying
the unit equation, but also approximation theorems due to Roth and Schmidt.