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arXiv · 1112.5579

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

Antonio Lei·David Loeffler·Sarah Livia Zerbes
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Abstract

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 the critical-slope L-function arising from Kato's Euler system and comparing this with results of Bellaiche on the critical-slope L-function defined using overconvergent modular symbols.

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Antonio Lei, David Loeffler, Sarah Livia Zerbes. 2011-12-23. Critical slope p-adic L-functions of CM modular forms. https://doi.org/10.1007/s11856-013-0020-0

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