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We present a new, simple proof, based upon Poisson summation, of the Lipschitz summation formula. A conceptually easy corollary is the functional relation for the Hurwitz zeta function. As a direct consequence we obtain a short, motivated proof of Riemann's functional equation for ((s). INTRODUCTION We present a short and motivated proof of Riemann's functional equation for Riemann's zeta function ((s) = EZ l ' initially defined in the half plane Re(s) > 1. In fact we prove the slightly more general functional relation for the Hurwitz zeta function

Easy proofs of Riemann’s functional equation for $\zeta (s)$ and of Lipschitz summation