On the Iwasawa invariants of a link in the 3-sphere

Based on the analogy between knots and primes, J. Hillman, D. Matei and M. Morishita defined the Iwasawa invariants for sequences of cyclic covers of links with an analogue of Iwasawa's class number formula of number fields. In this paper, we consider the existence of covers of links with prescribed Iwasawa invariants, discussing analogies in number theory. We also propose and consider a problem analogous to Greenberg's conjecture.