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**1 - 1**of**1**### ERGODICITY OF THE ACTION OF K ∗ ON AK

, 2013

"... Connes gave a spectral interpretation of the critical zeros of zeta- and L-functions for a global field K using a space of square integrable functions on the space AK/K ∗ of adele classes. It is known that for K = Q the spaceAK/K ∗ cannot be understood classically, or in other words, the action ofQ ..."

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Connes gave a spectral interpretation of the critical zeros of zeta- and L-functions for a global field K using a space of square integrable functions on the space AK/K ∗ of adele classes. It is known that for K = Q the spaceAK/K ∗ cannot be understood classically, or in other words, the action ofQ ∗ onAQ is ergodic. We prove that the same is true for any global field K, in both the number field and function field cases.