One valued primitives and the F. and M. Riesz theorem
  For a non-simply connected domain Omega in C and f a holomorphic function on Omega we prove that f admits one-valued primitives of any order in Omega, if and only if, it extends holomorphically in the simply connected envelope of Omega . This leads to a generalization of the F. and M. Riesz theorem. 
V. Nestoridis
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