For several large classes of functions in the infinite polydisk Hardy space, a function is cyclic if and only if it is zero-free, yielding complete solutions to the Periodic Dilation Completeness Problem in those cases.
B\' a ez-Duarte, A strengthening of the N yman- B eurling criterion for the R iemann hypothesis , Atti Accad
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The Periodic Dilation Completeness Problem: Cyclic vectors in the Hardy space over the infinite-dimensional polydisk
For several large classes of functions in the infinite polydisk Hardy space, a function is cyclic if and only if it is zero-free, yielding complete solutions to the Periodic Dilation Completeness Problem in those cases.