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Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes

2014; Institut de Mathématiques de Bordeaux; Volume: 26; Issue: 3 Linguagem: Inglês

10.5802/jtnb.885

2118-8572

Robert Harron, Antonio Lei,

Analytic Number Theory Research

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 conjectures of Dabrowski and Panchishkin in this special case. We combine this with recent work of Benois to prove the trivial zero conjecture in this setting. We also construct “mixed” plus and minus p-adic L-functions and prove an analogue of Pollack’s decomposition of the admissible p-adic L-functions. On the arithmetic side, we define corresponding mixed plus and minus Selmer groups and formulate the Main Conjecture of Iwasawa Theory.