Georgia Institute of Technology College of Sciences

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We discuss the Pointwise Ergodic Theorem for the Gaussian divisor function $d(n)$, that is, for a measure preserving $\mathbb Z [i]$ action $T$, the ergodic averages weighted by the divisor function converge pointwise for all functions in $L^p$, for $p>1$.  We obtain improving and sparse bounds for these averages.