Greenberg's conjecture for Dirichlet characters of order divisible by $p$
Tsuji, Takae
Proc. Japan Acad. Ser. A Math. Sci., Tome 77 (2001) no. 10, p. 52-54 / Harvested from Project Euclid
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Fix an odd prime number $p$. For an even Dirichlet character $\chi$, it is conjectured that the Iwasawa $\lambda$-invariant $\lambda_{p,\chi}$ related to the $\chi$-part of ideal class group is zero ([5], [2]). In this note, we show (under some assumptions) that there exist infinitely many characters $\chi$ of order divisible by $p$ for which the conjecture is true by using Kida's formula ([6]).
Publié le : 2001-04-14
Classification:  Iwasawa theory,  Greenberg's conjecture,  Kida's formula,  11R23 
@article{1148393080,
     author = {Tsuji, Takae},
     title = {Greenberg's conjecture for Dirichlet characters of order divisible by $p$},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {77},
     number = {10},
     year = {2001},
     pages = { 52-54},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148393080}
}

Tsuji, Takae. Greenberg's conjecture for Dirichlet characters of order divisible by $p$. Proc. Japan Acad. Ser. A Math. Sci., Tome 77 (2001) no. 10, pp.  52-54. http://gdmltest.u-ga.fr/item/1148393080/