Bounded <i>p</i>-adic <i>L</i>-functions of motives at supersingular primes

Dąbrowski, Andrzej

doi:10.1016/j.crma.2011.03.015

Number Theory

Bounded p-adic L-functions of motives at supersingular primes
[Fonctions L p-adiques bornées des motifs en une place très supersingulière]

Présenté par : Jean-Pierre Serre

Dąbrowski, Andrzej ¹

¹ Institute of Mathematics, University of Szczecin, ul. Wielkopolska 15, 70-451 Szczecin, Poland

Comptes Rendus. Mathématique, Tome 349 (2011) no. 7-8, pp. 365-368.

Résumé
Abstract

Dans [17] Pollack (2003) a montré que la fonction L p-adique associée à une forme modulaire $f = \sum a_{n} q^{n}$ en une place très supersingulière p ( $a_{p} = 0$ ) 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 $f = \sum a_{n} q^{n}$ at the most supersingular prime p (i.e. $a_{p} = 0$ ) 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).

Reçu le : 2010-06-10
Accepté le : 2011-03-15
Publié le : 2011-03-31

DOI : 10.1016/j.crma.2011.03.015

Affiliations des auteurs :

Dąbrowski, Andrzej ¹

¹ Institute of Mathematics, University of Szczecin, ul. Wielkopolska 15, 70-451 Szczecin, Poland

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Dąbrowski, Andrzej. Bounded p-adic L-functions of motives at supersingular primes. Comptes Rendus. Mathématique, Tome 349 (2011) no. 7-8, pp. 365-368. doi : 10.1016/j.crma.2011.03.015. http://www.numdam.org/articles/10.1016/j.crma.2011.03.015/

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