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Critical slope p-adic L-functions of CM modular forms


For ordinary modular forms, there are two constructions of a p-adic L-function attached to the non-unit root of the Hecke polynomial, which are conjectured but not known to coincide. We prove this conjecture for modular forms of CM type, by calculating the critical-slope L-function arising from Kato’s Euler system and comparing this with results of Bellaïche on the critical-slope L-function defined using overconvergent modular symbols.

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Correspondence to Antonio Lei.

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The first author is grateful for the support of a CRM-ISM postdoctoral fellowship.

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Lei, A., Loeffler, D. & Zerbes, S.L. Critical slope p-adic L-functions of CM modular forms. Isr. J. Math. 198, 261–282 (2013).

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  • Modular Form
  • Galois Group
  • Dirichlet Character
  • Modular Symbol
  • Iwasawa Theory