Open Access
Jan. 2003 $L_p(1,\chi) \bmod{p}$
Jangheon Oh
Proc. Japan Acad. Ser. A Math. Sci. 79(1): 11-13 (Jan. 2003). DOI: 10.3792/pjaa.79.11


In this paper, we compute $L_p(1, \chi) \bmod{p}$ when $\chi$ is the nontrivial character of a real quadratic field. As a result, we give a sufficient condition for Iwasawa invariants $\mu_p(k)$, $\lambda_p(k)$ to vanish when $p$ splits in a real quadratic field $k$.


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Jangheon Oh. "$L_p(1,\chi) \bmod{p}$." Proc. Japan Acad. Ser. A Math. Sci. 79 (1) 11 - 13, Jan. 2003.


Published: Jan. 2003
First available in Project Euclid: 18 May 2005

zbMATH: 1046.11080
MathSciNet: MR1953977
Digital Object Identifier: 10.3792/pjaa.79.11

Primary: 11R23
Secondary: 11S40

Keywords: Greenberg's conjecture , Iwasawa invariants , special value of $p$-adic $L$-function

Rights: Copyright © 2003 The Japan Academy

Vol.79 • No. 1 • Jan. 2003
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