Abstract: In 1996, Zoltán Buczolich proved a partial converse to Birkhoff's Ergodic theorem with periodic potential functions and a map that rotates the circle. In this talk we will present a generalization of this result to translation maps on the n-dimensional torus, and with a potential function on the n-dimensional torus. The proof of this result, as well as the original one, rely heavily on Fourier Analysis.