A note on Greenberg's conjecture and the abc conjecture

被引：4

作者：

Ichimura, H ^{[1
]}

机构：

[1] Yokohama City Univ, Dept Math, Kanazawa Ku, Yokohama, Kanagawa 236, Japan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1998年 / 126卷 / 05期

关键词：

D O I：

10.1090/S0002-9939-98-04196-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For any totally real number field Ic and any prime number p, Greenberg's conjecture for (k,p) asserts that the Iwasawa invariants lambda(p)(k) and mu(p)(k) are both zero. For a fixed real abelian field k, we prove that the conjecture is "affirmative" for infinitely many p (which split in k) if we assume the abe conjecture for k.

引用

页码：1315 / 1320

页数：6

共 10 条

[1]

Coates J., 1977, PADIC LFUNCTIONS IWA, P269

[2] IWASAWA INVARIANT MU-P VANISHES FOR ABELIAN NUMBER FIELDS [J].

FERRERO, B ;

WASHINGTON, LC .

ANNALS OF MATHEMATICS, 1979, 109 (02) :377-395

[3] ON ZP-EXTENSIONS OF REAL QUADRATIC FIELDS [J].

FUKUDA, T ;

KOMATSU, K .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1986, 38 (01) :95-102

[4]

GILLARD R, 1979, ANN I FOURIER, V29, P1, DOI DOI 10.5802/AIF.763

[5] IWASAWA INVARIANTS OF TOTALLY REAL NUMBER FIELDS [J].

GREENBERG, R .

AMERICAN JOURNAL OF MATHEMATICS, 1976, 98 (01) :263-284

[6] On the Iwasawa invariants of certain real abelian fields .2. [J].

Ichimura, H ;

Sumida, H .

INTERNATIONAL JOURNAL OF MATHEMATICS, 1996, 7 (06) :721-744

[7] ZL-EXTENSIONS OF ALGEBRAIC NUMBER FIELDS [J].

IWASAWA, K .

ANNALS OF MATHEMATICS, 1973, 98 (02) :246-326

[8] OLD AND NEW CONJECTURED DIOPHANTINE INEQUALITIES [J].

LANG, S .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 23 (01) :37-75

[9]

Vojta P., 1987, Lecture Notes in Mathematics, V1239

[10]

Washington L. C., 1982, GRAD TEXTS MATH, V83

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