Today I gave my talk in the Seminar on Irrationality and Transcendence (Number Theory) offered by Prof. Sander Zwegers (University of Cologne). In my talk I defined E-Functions, proved some properties, and derived the Lindemann-Weierstraß Theorem from Shidlovskii's Theorem. You are welcome to download the German presentation slides.
Today I gave my talk in the Proseminar on Partitions (Number Theory) offered by Prof. Kathrin Bringmann (University of Cologne). In my talk I gave a proof of the Jacobi Triple Product Identity and also proved some beautiful corollaries, e.g. Euler's Pentagonal Number Theorem.
Using the following definition of the Pochhammer Symbol
the Jacobi Triple Product Identity becomes
Using this equation, the Pentagonal Number Theorem
can be obtained by replacing by .