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A criterion for Greenberg's conjecture

Authors: Luca Caputo and Filippo Alberto Edoardo Nuccio
Journal: Proc. Amer. Math. Soc. 136 (2008), 2741-2744
MSC (2000): Primary 11R23; Secondary 11R70
Published electronically: April 3, 2008
MathSciNet review: 2399036
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Abstract: We give a criterion for the vanishing of the Iwasawa $ \lambda$-invariants of totally real number fields $ K$ based on the class number of $ K(\zeta_p)$ by evaluating the $ p$-adic $ L$-functions at $ s=-1$.

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Luca Caputo
Affiliation: Dipartimento di Matematica “Leonida Tonelli”, Università degli studi di Pisa, Largo Bruno Pontecorvo, 5 - 56127 - Pisa, Italy

Filippo Alberto Edoardo Nuccio
Affiliation: Dipartimento di Matematica “Guido Castelnuovo”, Università degli studi “La Sapienza” Piazzale Aldo Moro, 5 - 00185 - Roma, Italy

Keywords: Iwasawa theory, Greenberg's Conjecture, $K$-theory of Global Fields
Received by editor(s): June 8, 2007
Received by editor(s) in revised form: July 2, 2007
Published electronically: April 3, 2008
Additional Notes: The second author wishes to thank the “Laboratoire de Mathématiques Nicolas Oresme” de Caen for its kind hospitality during the period in which this work has been done.
Communicated by: Ken Ono
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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