-Invariants of Adjoint Square Galois Representations Coming from Modular Forms
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 
be a newform that is p-ordinary (i.e. 
is coprime to p), and 
the associated Galois representation. We find the special value 
. We define the analytic 
-invariant of a "motivic" Galois representation, and show how this special value relates to work of Greenberg and Hida on finding 
. 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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