Analysis Seminar: An ergodic theorem in the Gaussian integer setting

Abstract: We discuss the Pointwise Ergodic Theorem for the Gaussian divisor function d(n), that is, for a measure preserving Z[i] action T, the ergodic averages weighted by the divisor function converge pointwise for all functions in Lp, for p>1.  We also obtain improving and sparse bounds for these averages along the way. This is joint work with Hamed Mousavi and Nazar Miheisi.

Host: Alan Chang