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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn048, 12 pages, doi:10.1093/imrn/rnn048 published on May 22, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Formula -Invariants of Adjoint Square Galois Representations Coming from Modular Forms

Craig Citro

Department of Mathematics, University of California Los Angeles, Los Angeles, CA, 90095-1555, USA

Correspondence: Correspondence to be sent to: craigcitro{at}gmail.com

Let Formula be a newform that is p-ordinary (i.e. Formula is coprime to p), and Formula the associated Galois representation. We find the special value Formula . We define the analytic Formula -invariant of a "motivic" Galois representation, and show how this special value relates to work of Greenberg and Hida on finding Formula . In particular, we reduce finding this value to showing an equality of p-adic L-functions similar to a well-known relation of archimedean L-functions. This provides evidence for a conjecture of Greenberg, which is originally based on a conjecture of Mazur, Tate, and Teitelbaum.


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