Nous donnons une introduction terre à terre de la théorie des familles de formes modulaires, et discutons des démonstrations élémentaires de résultats suggérant que les formes modulaires apparaissent sous forme de familles.
We give a down-to-earth introduction to the theory of families of modular forms, and discuss elementary proofs of results suggesting that modular forms come in families.
@article{JTNB_2001__13_1_43_0, author = {Buzzard, Kevin}, title = {Families of modular forms}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {43--52}, publisher = {Universit\'e Bordeaux I}, volume = {13}, number = {1}, year = {2001}, mrnumber = {1838069}, zbl = {1052.11036}, language = {en}, url = {http://www.numdam.org/item/JTNB_2001__13_1_43_0/} }
Buzzard, Kevin. Families of modular forms. Journal de théorie des nombres de Bordeaux, Tome 13 (2001) no. 1, pp. 43-52. http://www.numdam.org/item/JTNB_2001__13_1_43_0/
[C] p-adic Banach spaces and families of modular forms. Invent. Math. 127 (1997), 417-479. | MR | Zbl
,[CM] The eigencurve. In Galois representations in arithmetic algebraic geometry (Durham, 1996), CUP 1998, 1-113. | MR | Zbl
, ,[GM] Families of modular eigenforms. Math. Comp. 58 no. 198 (1992), 793-805. | MR | Zbl
, ,[S] Introduction to the arithmetic theory of automorphic functions. Princeton University Press, 1994. | MR | Zbl
,[T] Princeton PhD thesis.
,[U] Slopes of modular forms. Contemp. Math. 174 (1994), 167-183. | MR | Zbl
,[W] Dimension variation of classical and p-adic modular forms. Invent. Math. 133 (1998), 449-463. | MR | Zbl
,