On Small Iwasawa Invariants and Imaginary Quadratic Fields

Heuristics for class numbers and lambda invariants

Let K = Q( √ −d) be an imaginary quadratic field and let Q( √ 3d) be the associated real quadratic field. Starting from the Cohen-Lenstra heuristics and Scholz’s theorem, we make predictions for the behaviors of the 3-parts of the class groups of these two fields as d varies. We deduce heuristic predictions for the behavior of the Iwasawa λ-invariant for the cyclotomic Z3extension of K and test...

On the non-triviality of the basic Iwasawa λ-invariant for an infinitude of imaginary quadratic fields

Computation of Iwasawa ν-invariants of certain real abelian fields

Let p be a prime number and k a finite extension of Q. It is conjectured that Iwasawa invariants λp(k) and μp(k) vanish for all p and totally real number fields k. Using cyclotomic units and Gauss sums, we give an effective method for computing the other Iwasawa invariants νp(k) of certain real abelian fields. As numerical examples, we compute Iwasawa invariants associated to k = Q( √ f, ζp + ζ...

J ul 2 00 8 On fake Z p - extensions of number fields

For an odd prime number p, let Fanti be the Zp-anticyclotomic extension of an imaginary quadratic field F . We focus on the non-normal subextension K∞ of Fanti fixed by a subgroup of order 2 in Gal(Fanti/Q). After providing a general result for dihedral extensions, we study the growth of the p-part of the class group of the subfields ofK∞/Q, providing a formula of Iwasawa type. Furthermore, we ...

On the real quadratic fields with certain continued fraction expansions and fundamental units

The purpose of this paper is to investigate the real quadratic number fields $Q(sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element  where $dequiv 2,3( mod  4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit$$epsilon _{d}=left(t_d+u_dsqrt{d}right) 2left.right > 1$$and  $n_d$ and $m_d...