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April 2001 Greenberg's conjecture for Dirichlet characters of order divisible by $p$
Takae Tsuji
Proc. Japan Acad. Ser. A Math. Sci. 77(4): 52-54 (April 2001). DOI: 10.3792/pjaa.77.52

Abstract

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]).

Citation

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Takae Tsuji. "Greenberg's conjecture for Dirichlet characters of order divisible by $p$." Proc. Japan Acad. Ser. A Math. Sci. 77 (4) 52 - 54, April 2001. https://doi.org/10.3792/pjaa.77.52

Information

Published: April 2001
First available in Project Euclid: 23 May 2006

zbMATH: 1061.11062
MathSciNet: MR1829374
Digital Object Identifier: 10.3792/pjaa.77.52

Subjects:
Primary: 11R23

Keywords: Greenberg's conjecture , Iwasawa theory , Kida's formula

Rights: Copyright © 2001 The Japan Academy

Vol.77 • No. 4 • April 2001
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