Complex analysis in transcendental number theory – the Gelfond-Schneider Theorem
Mr. Tsz On Chan
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: |
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Time: |
4:00 – 5:00pm |
Place: |
Room 517, Meng Wah Complex |
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All are welcome |
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