The Riemann zeta function and its special values at even integers -- Thibaut Pugin
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I would define the zeta function, prove that it has a meromorphic
extension to the complex numbers and maybe mention one or two theorems
related to it (like, about prime numbers). Then we would prove the
formula zeta (2k) = -1/2 B_{2k} (2i)^{2k} / (2k)! where B_{2k}
are the Bernouilli numbers. Nothing is hard here.