TY - JOUR
T1 - Construction of Zp -extensions with prescribed Iwasawa λ-invariants
AU - Fujii, Satoshi
AU - Ohgi, Yoshihiro
AU - Ozaki, Manabu
N1 - Funding Information:
* Corresponding author. E-mail addresses: fujii@ruri.waseda.jp (S. Fujii), ozaki@math.kindai.ac.jp (M. Ozaki). 1 The author was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B), 15740016, 2005.
PY - 2006/6
Y1 - 2006/6
N2 - It is a basic problem in Iwasawa theory that the existence of a Zp-extension with prescribed Iwasawa invariants. Since the Iwasawa λ-invariant is regarded as an analogue of (twice of) the genus of an algebraic curve, we are especially interested in the problem on the Iwasawa λ-invariants. In this article, for a few prime numbers p, we show that there is a Zp-extension with prescribed Iwasawa λ-invariant by using Kida's formula, which is a number field analogue of the Riemann-Hurwitz formula.
AB - It is a basic problem in Iwasawa theory that the existence of a Zp-extension with prescribed Iwasawa invariants. Since the Iwasawa λ-invariant is regarded as an analogue of (twice of) the genus of an algebraic curve, we are especially interested in the problem on the Iwasawa λ-invariants. In this article, for a few prime numbers p, we show that there is a Zp-extension with prescribed Iwasawa λ-invariant by using Kida's formula, which is a number field analogue of the Riemann-Hurwitz formula.
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U2 - 10.1016/j.jnt.2005.09.004
DO - 10.1016/j.jnt.2005.09.004
M3 - Article
AN - SCOPUS:33646111912
SN - 0022-314X
VL - 118
SP - 200
EP - 207
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 2
ER -