Geodesic
Factorisation of Two-variable p-adic L-functions
Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 845-852

Voir la notice de l'article provenant de la source Cambridge University Press

Let $f$ be a modular form that is non-ordinary at $p$ . Loeffler has recently constructed four two-variable $p$ -adic $L$ -functions associated with $f$ . In the case where ${{a}_{p}}\,=\,0$ , he showed that, as in the one-variable case, Pollack’s plus and minus splitting applies to these new objects. In this article, we show that such a splitting can be generalised to the case where ${{a}_{p}}\ne 0$ using Sprung’s logarithmic matrix.
DOI : 10.4153/CMB-2013-044-2
Mots-clés : 11S40, 11S80, modular forms, p-adic L-functions, supersingular primes 
Lei, Antonio. Factorisation of Two-variable p-adic L-functions. Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 845-852. doi: 10.4153/CMB-2013-044-2
@article{10_4153_CMB_2013_044_2,
     author = {Lei, Antonio},
     title = {Factorisation of {Two-variable} p-adic {L-functions}},
     journal = {Canadian mathematical bulletin},
     pages = {845--852},
     year = {2014},
     volume = {57},
     number = {4},
     doi = {10.4153/CMB-2013-044-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-044-2/}
}
TY  - JOUR
AU  - Lei, Antonio
TI  - Factorisation of Two-variable p-adic L-functions
JO  - Canadian mathematical bulletin
PY  - 2014
SP  - 845
EP  - 852
VL  - 57
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-044-2/
DO  - 10.4153/CMB-2013-044-2
ID  - 10_4153_CMB_2013_044_2
ER  - 
%0 Journal Article
%A Lei, Antonio
%T Factorisation of Two-variable p-adic L-functions
%J Canadian mathematical bulletin
%D 2014
%P 845-852
%V 57
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-044-2/
%R 10.4153/CMB-2013-044-2
%F 10_4153_CMB_2013_044_2

[AV75] [AV75] Amice, Y. and Vélu, J., Distributions p-adiques associées aux séries de Hecke. In: Journées Arithmétiques de Bordeaux (Conf., Univ. Bordeaux, Bordeaux, 1974), Astérisque, 24–25, Soc. Math. France, Paris, 1975, pp. 119–131. Google Scholar

[CB98] [CB98] Coleman, R. and Edixhoven, B., On the semi-simplicity of the up-operator on modular forms.Math. Ann. 310 (1998), no 1, 119–127. Google Scholar | DOI

[Kim11] [Kim11] Kim, B. D., Two-variable p-adic L-functions of modular forms for non-ordinary primes. Preprint. http://homepages.ecs.vuw.ac.nz/_bdkim/BDKim-2011-1.pdf Google Scholar

[LLZ10] [LLZ10] Lei, A., Loeffler, D., and Zerbes, S. L., Wach modules and Iwasawa theory for modular forms.Asian J. Math. 14 (2010), no. 4, 475–528. Google Scholar | DOI

[Loe13] [Loe13] Loeffler, D., p-adic integration on ray class groups and non-ordinary p-adic L-functions. arxiv:1304.4042, 2013. Google Scholar

[PR94] [PR94] Perrin-Riou, B., Théorie d’Iwasawa des représentations p-adiques sur un corps local.Invent. Math. 115 (1994), no. 1, 81–161. Google Scholar | DOI

[Pol03] [Pol03] Pollack, R., On the p-adic L-function of a modular form at a supersingular prime.Duke Math. J. 118 (2003), no. 3, 523–558. Google Scholar | DOI

[Spr12a] [Spr12a] Sprung, F., On pairs of p-adic analogues of the conjectures of Birch and Swinnerton-Dyer http://arxiv:1211.1352, 2012. Google Scholar

[Spr12b] [Spr12b] Sprung, F., Iwasawa theory for elliptic curves at supersingular primes: a pair of main conjectures.J. Number Theory 132 (2012), no. 7, 1483–1506. Google Scholar | DOI

[Viš76] [Viš76] Višik, M. M., Nonarchimedean measures associated with Dirichlet series.Mat. Sb. (N.S.) 99(141) (1976), no. 2, 248–260, 296. Google Scholar

Cité par Sources :