Abstract:  

In this short course, we introduce an elementary approach to the irrationality of the values of the Riemann zeta function at positive odd integers (＞1). We explain the results of  Apéry (1979), Ball-Rivoal(2001), Zudilin(2001), Fischler-Sprang-Zudilin/Lai-Yu(2019/2020) and Lai(2024+) in a systematic way. The routine of the proofs is "Rational functions → Linear forms → Irrationality". We focus on the ideas of constructing rational functions. 

This course is friendly to undergraduates. No prior knowledge is required except for elementary number theory and complex  analysis.

Time:

Beginning September 17, and there will be five sessions on Tuesdays from 3:10-5:00pm.