Geodesic
A Note on p-adic Rankin–Selberg L-functions
Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 608-621

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

We prove an interpolation formula for the values of certain $p$ -adic Rankin-Selberg $L$ -functions associated with non-ordinary modular forms.
DOI : 10.4153/CMB-2017-047-9
Mots-clés : 11F85, 11F67, 11G40, 14G35, p-adic L-function, Iwasawa theory 
Loeffler, David. A Note on p-adic Rankin–Selberg L-functions. Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 608-621. doi: 10.4153/CMB-2017-047-9
@article{10_4153_CMB_2017_047_9,
     author = {Loeffler, David},
     title = {A {Note} on p-adic {Rankin{\textendash}Selberg} {L-functions}},
     journal = {Canadian mathematical bulletin},
     pages = {608--621},
     year = {2018},
     volume = {61},
     number = {3},
     doi = {10.4153/CMB-2017-047-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-047-9/}
}
TY  - JOUR
AU  - Loeffler, David
TI  - A Note on p-adic Rankin–Selberg L-functions
JO  - Canadian mathematical bulletin
PY  - 2018
SP  - 608
EP  - 621
VL  - 61
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-047-9/
DO  - 10.4153/CMB-2017-047-9
ID  - 10_4153_CMB_2017_047_9
ER  - 
%0 Journal Article
%A Loeffler, David
%T A Note on p-adic Rankin–Selberg L-functions
%J Canadian mathematical bulletin
%D 2018
%P 608-621
%V 61
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-047-9/
%R 10.4153/CMB-2017-047-9
%F 10_4153_CMB_2017_047_9

[AI17] [AI17] Andreatta, F. and Iovita, A. (with an appendix by Eric Urban), Triple product p-adic L-functions associated tofinite slope p-adic families of modularforms. arxiv:1708.02785 Google Scholar

[BDR15a] [BDR15a] Bertolini, M., Darmon, H., and Rotger, V., Beiünson-Flach elements and Euler Systems I: syntomic regulators and p-adic Rankin L-series. J. Algebraic Geom. 24(2015), no. 2, 355–378. http://dx.doi.Org/10.1090/S1056-3911-2014-00670-6 Google Scholar

[BDR15b] [BDR15b] Bertolini, M., Beilinson-Flach elements and Euler Systems II: the Birch and Swinnerton-Dyer conjectureforHasse-Weil-Artin L-functions. J. Algebraic Geom. 24(2015), no. 3, 569–604. http://dx.doi.Org/10.1090/S1056-3911-2015-00675-0 Google Scholar

[BL16a] [BL16a] Büyükboduk, K. and Lei, A., Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms. arxiv:1 602.07508 Google Scholar

[BL16b] [BL16b] Büyükboduk, K. and Lei, A., Anticyclotomic Iwasawa theory of elliptic modular forms at non-ordinary primes. arxiv:1 605.05310 Google Scholar

[Casl5] [Casl5] Castella, F., p-adic heights of Heegner points and Beilinson-Flach classes. J. London Math. Soc. 96(2017), no.1, 156–180. http://dx.doi.Org/10.1112/jlms.1 2058 Google Scholar

[CE98] [CE98] Coleman, R. F. and Edixhoven, B., On the semi-simplicity ofthe Up-operator on modular forms. Math. Ann. 310(1998), no. 1, 119–127. http://dx.doi.Org/10.1007/s002080050140 Google Scholar

[Dasl6] [Dasl6] Dasgupta, S., Factorization ofp-adic Rankin L-series. Invent. Math. 205(2016), no. 1, 221–268. http://dx.doi.Org/10.1OO7/sOO222-O15-0634-4 Google Scholar

[Hid85] [Hid85] Hida, H., A p-adic measure attached to the zeta functions associated with two elüptic modular forms. I. Invent. Math. 79(1985), no. 1, 159–195. http://dx.doi.Org/10.1007/BF01388661 Google Scholar

[Hid88] [Hid88] Hida, H., A p-adic measure attached to the zeta functions associated with two elüptic modular forms. II. Ann. Inst. Fourier (Grenoble) 38(1988), no. 3, 1–83. http://dx.doi.Org/10.58O2/aif.1141 Google Scholar

[JSW15] [JSW15] Jetchev, D., Skinner, C., and Wan, X., The Birch-Swinnerton-Dyer formula for elüptic curves of analytic rank one. arxiv:1512.06894 Google Scholar

[KatO4] [KatO4] Kato, K., P-adic Hodge theory and values of zeta functions of modular forms. Cohomologies p-adiques et applications arithmetiques. III. Asterisque 295(2004), ix, 117–290. Google Scholar

[KLZ17] [KLZ17] Kings, G., Loeffler, D., and Zerbes, S. L., Rankin-Eisenstein classes and explicit reciprocity laws. Cambridge J. Math. 5(2017), no. 1, 1–122. http://dx.doi.Org/10.4310/CJM.2017.v5.n1.a1 Google Scholar

[LLZ14] [LLZ14] Lei, A., Loeffler, D., and Zerbes, S. L., Euler Systems for Rankin-Selberg convolutions of modular forms. Ann. of Math. (2) 180(2014), no. 2, 653–771. http://dx.doi.Org/10.4007/annals.2014.1 80.2.6 Google Scholar

[LZ16] [LZ16] Loeffler, D. and Zerbes, S. L., Rankin-Eisenstein classes in Coleman families. Res. Math. Sei. 3(2016), no. 29, 53. http://dx.doi.Org/10.1186/s40687-016-0077-6 Google Scholar

[My91] [My91] My, V. K., Rankin non-Archimedean convolutions of unbounded growth. Mat. Sb. (N.S.) 182(1991), no. 2,164-174; translation in Math. USSR-Sb. 72(1992), no. 1, 151–161. Google Scholar

[OhtOO] [OhtOO] Ohta, M., Ordinary p-adic etale cohomology groups attached to towers ofelliptic modular curves. II. Math. Ann. 318(2000), no. 3, 557–583. http://dx.doi.Org/10.1007/s002080000119 Google Scholar

[Pan82] [Pan82] Panchishkin, A., Leprolongement p-adique analytique des fonetions L de Rankin. I. C. R. Acad. Sei. Paris Ser. I Math. 295(1982), no. 2, 51–53. Google Scholar

[PR88] [PR88] Perrin-Riou, B., Fonetions L p-adiques associees ä une forme modulaire et ä un corps quadratique imaginaire. J. London Math. Soc. 38(1988), no. 1, 1–32. http://dx.doi.Org/10.1112/jlms/s2-38.1.1 Google Scholar

[Urbl4] [Urbl4] Urban, E., Nearly overconvergent modular forms. In: Iwasawa Theory 2012: State ofthe Art and Recent Advances, Springer Berlin, Heidelberg, 2014, pp. 401–441. http://dx.doi.org/10.1007/978-3-642-55245-8J4 Google Scholar

[Wanl5] [Wanl5] Wan, X., Iwasawa main conjeeturefor supersingular elüptic curves. arxiv:1411.6352v2 Google Scholar

Cité par Sources :