Noncyclotomic Z_p-Extensions of Imaginary Quadratic Fields

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 invariants
• Siegel function
• computation