BOTH MAYOR Barry and the man who for years has been conducting investigations of him and his administration, U.S. Attorney Joseph E. diGenova, have stated that they do not expect Mr. diGenova's departure from office to curtail these activities. In his letter of resignation to President Reagan, Mr. diGenova said he was "confident" that the U.S. attorney's office would continue to pursue "the work already under way, particularly the necessary effort against local public corruption." Though these investigations have resulted in convictions of top Barry administration officials on corruption charges, Mr. Barry and other city officials have complained over the years about "prosecutorial abuse and vindictiveness" -- and have challenged federal prosecutors still pursuing investigations to put up or lay off. Meanwhile, everybody else wonders what's really going on; curiosity and a shortage of hard facts continue to stir up suspicions, rumors and sweeping but groundless assumptions about the ethics of city hall employees up and down the ranks. Whatever the truth, when will these investigations be completed?

None of those who might know is saying -- which leaves the city government under a giant cloud. Will the federal investigators start showing their cards by March 1, the effective date of Mr. diGenova's resignation? Or will there be some indictments or guilty pleas six months from now? Or should the city steel itself for years of leaks, allegations and hints of impending announcements?

It isn't a matter of accusing the U.S. attorney of playing games, because there is no accurate way of knowing precisely what it is the investigations have produced or will lead to. But it isn't enough for the U.S. attorney's office -- under anyone -- to carry on indefinitely without some kinds of status reports to the public, reports that should jeopardize neither the investigations nor the rights of those involved. No matter where any of this leads, the sooner the work is completed the better this city and its government will be.