The relevant statute is Arizona Revised Statutes Section 14-3801. It states:
A. Unless notice has already been given under this section, at the
time of appointment a personal representative shall publish a notice
to creditors once a week for three successive weeks in a newspaper of
general circulation in the county announcing the appointment and the
personal representative's address and notifying creditors of the
estate to present their claims within four months after the date of
the first publication of the notice or be forever barred.
B. A personal representative shall give written notice by mail or
other delivery to all known creditors, notifying the creditors of the
personal representative's appointment. The notice shall also notify
all known creditors to present the creditor's claim within four months
after the published notice, if notice is given as provided in
subsection A, or within sixty days after the mailing or other delivery
of the notice, whichever is later, or be forever barred. A written
notice shall be the notice described in subsection A or a similar
C. The personal representative is not liable to a creditor or to a
successor of the decedent for giving or failing to give notice under
So, while it is mandatory to do so, the obligation to do so arises only once you have been appointed as personal representative. Also, while the probate court could revoke your letters of appointment for not making a publication as required by statute, there is no legal liability of the personal representative to third parties for failing to do so.
And, it might be possible to waive this requirement, if all creditors of the estate were barred anyway, for example, because the estate has no assets that are not exempt from creditor's claims, or because all outstanding claims which might have been brought against the estate are barred pursuant to Arizona Revised Statutes Section 14-3803 with the adjustments to the statutes of limitations of Section 14-3802.