The Riemann zeta function: Analytic continuation and the functional equation

In this talk, we discuss about some well-known properties of the celebrated Riemann zeta function such as: analytic continuation and the functional equation. We will cosely follow Riemann's own proof from his infamous 1859 paper.

 In the proof of the above mentioned results we use elementary techniques from harmonic analysis such as theta functions, Mellin and Fourier transforms or Poisson summation formula.