I have a field that is the sum of 3 other fields. How do I leave the field blank if the value is zero?

Are you using a script for the calculation, or something else?

If you're not using a script, you'll need to. The basic code to achieve it is:

var v1 = Number(this.getField("Text1").valueAsString);
var v2 = Number(this.getField("Text2").valueAsString);
var v3 = Number(this.getField("Text3").valueAsString);
var total = v1+v2+v3;
event.value = (total==0) ? "" : total;