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In 1979 I. Cior\u{a}nescu and L. Zsid\'o have proved a minimum modulustheorem for entire functions dominated by the restriction to the positive halfaxis of a canonical product of genus zero, having all roots on the positiveimaginary axis and satisfying a certain condition.  Here we prove that the above result is optimal: if a canonical product{\omega} of genus zero, having all roots on the positive imaginary axis, doesnot satisfy the condition in the 1979 paper, then always there exists an entirefunction dominated by the restriction to the positive half axis of {\omega},which does not satisfy the desired minimum modulus conclusion. This hasrelevant implication concerning the subjectivity of ultra differentialoperators with constant coefficients.

A negative minimum modulus theorem and surjectivity of ultradifferential operators