Families of modular forms
Journal de théorie des nombres de Bordeaux, Volume 13 (2001) no. 1, p. 43-52

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.

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.

@article{JTNB_2001__13_1_43_0,
     author = {Buzzard, Kevin},
     title = {Families of modular forms},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {13},
     number = {1},
     year = {2001},
     pages = {43-52},
     zbl = {1052.11036},
     mrnumber = {1838069},
     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, Volume 13 (2001) no. 1, pp. 43-52. http://www.numdam.org/item/JTNB_2001__13_1_43_0/

[C] R. Coleman, p-adic Banach spaces and families of modular forms. Invent. Math. 127 (1997), 417-479. | MR 1431135 | Zbl 0918.11026

[CM] R. Coleman, B. Mazur, The eigencurve. In Galois representations in arithmetic algebraic geometry (Durham, 1996), CUP 1998, 1-113. | MR 1696469 | Zbl 0932.11030

[GM] F. Gouvêa, B. Mazur, Families of modular eigenforms. Math. Comp. 58 no. 198 (1992), 793-805. | MR 1122070 | Zbl 0773.11030

[S] G. Shimura, Introduction to the arithmetic theory of automorphic functions. Princeton University Press, 1994. | MR 1291394 | Zbl 0872.11023

[T] R. Taylor, Princeton PhD thesis.

[U] D. Ulmer, Slopes of modular forms. Contemp. Math. 174 (1994), 167-183. | MR 1299742 | Zbl 0853.11037

[W] D. Wan, Dimension variation of classical and p-adic modular forms. Invent. Math. 133 (1998), 449-463. | MR 1632794 | Zbl 0907.11016