Critical slope p -adic L -functions of CM modular forms
Identifieur interne : 000090 ( Main/Exploration ); précédent : 000089; suivant : 000091Critical slope p -adic L -functions of CM modular forms
Auteurs : Antonio Lei [Canada] ; David Loeffler [Royaume-Uni] ; Sarah Livia Zerbes [Royaume-Uni]Source :
- Israel Journal of Mathematics [ 0021-2172 ] ; 2013-11-01.
Abstract
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 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.
Url:
DOI: 10.1007/s11856-013-0020-0
Affiliations:
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J. Math.</title><idno type="ISSN">0021-2172</idno><idno type="eISSN">1565-8511</idno><imprint><publisher>Springer US; http://www.springer-ny.com</publisher><pubPlace>Boston</pubPlace><date type="published" when="2013-11-01">2013-11-01</date><biblScope unit="volume">198</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="261">261</biblScope><biblScope unit="page" to="282">282</biblScope></imprint><idno type="ISSN">0021-2172</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0021-2172</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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. 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