## Experimental Mathematics

- Experiment. Math.
- Volume 11, Issue 4 (2002), 469-475.

### Noncyclotomic $\Z_p$-Extensions of Imaginary Quadratic Fields

Takashi Fukuda and Keiichi Komatsu

#### 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 $\mu$ and $\lambda$ both vanish
for these specfic noncyclotomic $\Z_p$-extensions.

#### Article information

**Source**

Experiment. Math., Volume 11, Issue 4 (2002), 469-475.

**Dates**

First available in Project Euclid: 10 July 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1057864657

**Mathematical Reviews number (MathSciNet)**

MR1969639

**Zentralblatt MATH identifier**

1162.11390

**Subjects**

Primary: 11G15: Complex multiplication and moduli of abelian varieties [See also 14K22] 11R27: Units and factorization 1140

**Keywords**

Iwasawa invariants Siegel function computation

#### Citation

Fukuda, Takashi; Komatsu, Keiichi. Noncyclotomic $\Z_p$-Extensions of Imaginary Quadratic Fields. Experiment. Math. 11 (2002), no. 4, 469--475. https://projecteuclid.org/euclid.em/1057864657