Let p be an odd prime number which splits into two distinct primes in an imaginary quadratic field K. Then K has certain kinds of noncyclotomic $\Z_p$-extensions which are constructed through ray class fields with respect to a prime ideal lying above p. We try to show that Iwasawa invariants $\mu$ and $\lambda$ both vanish for these specfic noncyclotomic $\Z_p$-extensions.
"Noncyclotomic $\Z_p$-Extensions of Imaginary Quadratic Fields." Experiment. Math. 11 (4) 469 - 475, 2002.