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

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.

14 pages

Cited by in corpus (2)

• Iwasawa theory and p-adic L-functions over ${\mathbf{Z}}_p^2$-extensions
• Arithmetic of critical $p$-adic $L$-functions