[Fonctions L p-adiques bornées des motifs en une place très supersingulière]
Dans [17] Pollack (2003) a montré que la fonction L p-adique associée à une forme modulaire en une place très supersingulière p () est contrôlée par deux fonctions dʼIwasawa et deux semi-logarithmes. Nous énonc˛ons une généralisation conjecturale des résultats de Pollack aux fonctions L p-adiques des motifs. Nous donnons divers exemples (produits symétriques et produits tensoriels de formes modulaires) qui confirment cette conjecture.
Pollack (2003) [17] proved that the p-adic L-function attached to a modular form at the most supersingular prime p (i.e. ) is controlled by two Iwasawa functions and by two half-logarithms. We formulate a (conjectural) generalization of this result to p-adic L-functions attached to motives, and give examples confirming our expectation (symmetric powers and tensor products of modular forms).
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@article{CRMATH_2011__349_7-8_365_0,
author = {Andrzej D\k{a}browski},
title = {Bounded \protect\emph{p}-adic {\protect\emph{L}-functions} of motives at supersingular primes},
journal = {Comptes Rendus. Math\'ematique},
pages = {365--368},
publisher = {Elsevier},
volume = {349},
number = {7-8},
year = {2011},
doi = {10.1016/j.crma.2011.03.015},
language = {en},
}
Andrzej Dąbrowski. Bounded p-adic L-functions of motives at supersingular primes. Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 365-368. doi : 10.1016/j.crma.2011.03.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.015/
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