Buzzard: Families of modular forms

Table of contents for this issue | Previous article | Next article

Kevin Buzzard
Families of modular forms
Journal de théorie des nombres de Bordeaux, 13 no. 1 (2001), p. 43-52
Article PDF | Reviews MR 1838069 | Zbl 1052.11036

Résumé - Abstract

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.

Bibliography

[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