Noncyclotomic Z_<i>p</i>-Extensions of Imaginary Quadratic Fields

Abstract

Abstract 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 μ and λ both vanish for these specfic noncyclotomic Z p -extensions. Keywords: Iwasawa invariantsSiegel functioncomputation