Families of modular forms

Kevin Buzzard

Journal de théorie des nombres de Bordeaux (2001)

  • Volume: 13, Issue: 1, page 43-52
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Buzzard, Kevin. "Families of modular forms." Journal de théorie des nombres de Bordeaux 13.1 (2001): 43-52. <http://eudml.org/doc/248710>.

@article{Buzzard2001,
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.},
author = {Buzzard, Kevin},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {-adic family of modular forms; operator; Newton polygon},
language = {eng},
number = {1},
pages = {43-52},
publisher = {Université Bordeaux I},
title = {Families of modular forms},
url = {http://eudml.org/doc/248710},
volume = {13},
year = {2001},
}

TY - JOUR
AU - Buzzard, Kevin
TI - Families of modular forms
JO - Journal de théorie des nombres de Bordeaux
PY - 2001
PB - Université Bordeaux I
VL - 13
IS - 1
SP - 43
EP - 52
AB - 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.
LA - eng
KW - -adic family of modular forms; operator; Newton polygon
UR - http://eudml.org/doc/248710
ER -

References

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  1. [C] R. Coleman, p-adic Banach spaces and families of modular forms. Invent. Math.127 (1997), 417-479. Zbl0918.11026MR1431135
  2. [CM] R. Coleman, B. Mazur, The eigencurve. In Galois representations in arithmetic algebraic geometry (Durham, 1996), CUP1998, 1-113. Zbl0932.11030MR1696469
  3. [GM] F. Gouvêa, B. Mazur, Families of modular eigenforms. Math. Comp.58 no. 198 (1992), 793-805. Zbl0773.11030MR1122070
  4. [S] G. Shimura, Introduction to the arithmetic theory of automorphic functions. Princeton University Press, 1994. Zbl0872.11023MR1291394
  5. [T] R. Taylor, Princeton PhD thesis. 
  6. [U] D. Ulmer, Slopes of modular forms. Contemp. Math.174 (1994), 167-183. Zbl0853.11037MR1299742
  7. [W] D. Wan, Dimension variation of classical and p-adic modular forms. Invent. Math.133 (1998), 449-463. Zbl0907.11016MR1632794

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