  Let f be a cuspidal newform with complex multiplication (CM) and let p be an
odd prime at which f is non-ordinary. We construct admissible p-adic
L-functions for the symmetric powers of f, thus verifying general conjectures
of Dabrowski and Panchishkin in this special case. We also construct their
"mixed" plus and minus counterparts and prove an analogue of Pollack's
decomposition of the admissible p-adic L-functions into mixed plus and minus
p-adic L-functions. On the arithmetic side, we define corresponding mixed plus
and minus Selmer groups. We unite the arithmetic with the analytic by first
formulating the Main Conjecture of Iwasawa Theory relating the plus and minus
Selmer groups with the plus and minus p-adic L-functions, and then proving the
exceptional zero conjecture for the admissible p-adic L-functions. The latter
result takes advantage of recent work of Benois, while the former uses recent
work of the second author, as well as the main conjecture of Mazur-Wiles.

Number Theory