According to the IRS, you should report all of your income on your tax return.
If, however, you receive a tax form (K-1) that doesn't appear to report any income then it is up to you whether to report that form or not.
From what you describe, this form may have been generated to report amounts that round down to "0" (i.e. less than $1). This would explain seeing "0s" where a value should be displayed.
If the IRS thinks otherwise - after matching their records with your return - they may send you an automated Notice of Proposed Increase in Taxes later this year. This is not an audit and is a very common occurrence.
They will calculate any tax due (plus interest and penalties) and you can send them a check (no amended return necessary).
