Geometry Seminar

Complex analysis in transcendental number theory – the Gelfond-Schneider Theorem

 

Mr. Tsz On Chan

The University of Hong Kong

 

 

Abstract

 

In proving the transcendence of αβ, Gelfond and Schneider considered values of meromorphic functions satisfying differential equations. With Schneider’s attempt to axiomatize, and Lang’s simplification, the method used is now called the “Schneider-Lang criterion”, which included the transcendence of e and π as a corollary. The proof of the “criterion” involves only a simple tool in complex analysis of one variable, namely, the maximum modulus principle. The proof of the “criterion” is presented to demonstrate the simple but essential linkage between complex analysis and transcendental number theory.

 

 

 

 

Date:

February 23, 2006 (Thursday)

Time:

4:00 – 5:00pm

Place:

Room 517, Meng Wah Complex

 

 

 

 

All are welcome