Planted inside or outside?
Where are you, and what's the weather been like there?
Watering? How much? How often?
After three weeks I'd probably succumb to digging in to check on them. I'm NOT saying that that's the right thing to do, I'm just saying that I'd probably do it, being the weak-willed individual that I am. I had my rhizomes in a planter indoors for two weeks before I dug to check why the Cascades were the only ones not doing anything. One rhizome (the weakest of the bunch) still hasn't done anything. The other (the strongest of the bunch, I got two each of three varieties) had a few good sprouts, which all seemed to be happily burrowing towards the center of the earth, as I'd planted it sprout-side-down.
Just my 2 cents. My experience is minimal. I figure that those on the board with more experience will want same answers to those first few questions, though.