Class numbers and Iwasawa invariants

of quadratic fields

Author:
James S. Kraft

Journal:
Proc. Amer. Math. Soc. **124** (1996), 31-34

MSC (1991):
Primary 11R11, 11R23, 11R29

MathSciNet review:
1301510

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let and be quadratic fields with 2 (mod 3) a positive integer. Let be the respective Iwasawa -invariants of the cyclotomic -extension of these fields. We show that if , then 3 does not divide the class number of and .

**1**Kuniaki Horie,*A note on basic Iwasawa 𝜆-invariants of imaginary quadratic fields*, Invent. Math.**88**(1987), no. 1, 31–38. MR**877004**, 10.1007/BF01405089**2**Kenkichi Iwasawa,*A note on class numbers of algebraic number fields*, Abh. Math. Sem. Univ. Hamburg**20**(1956), 257–258. MR**0083013****3**N. Jochnowitz,*A -adic conjecture about derivatives of -series attatched to modular forms*, Proceedings of the Boston University Conference on -Adic Monodromy and the -Adic Birch and Swinnerton-Dyer Conjecture (to appear), CMP**94:13**.**4**------,*An alternative approach to non-vanishing theorems for coefficients of half integral weight forms mod and implications for Iwasawa's -invariant for quadratic fields*(to appear).**5**Lawrence C. Washington,*Zeros of 𝑝-adic 𝐿-functions*, Seminar on Number Theory, Paris 1980-81 (Paris, 1980/1981) Progr. Math., vol. 22, Birkhäuser, Boston, Mass., 1982, pp. 337–357. MR**693329****6**Lawrence C. Washington,*Introduction to cyclotomic fields*, Graduate Texts in Mathematics, vol. 83, Springer-Verlag, New York, 1982. MR**718674**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
11R11,
11R23,
11R29

Retrieve articles in all journals with MSC (1991): 11R11, 11R23, 11R29

Additional Information

**James S. Kraft**

Email:
kraft@ithaca.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03085-7

Received by editor(s):
September 1, 1993

Received by editor(s) in revised form:
August 1, 1994

Communicated by:
William Adams

Article copyright:
© Copyright 1996
American Mathematical Society