Geometric and p -adic Modular Forms of Half-Integral Weight

Nick Ramsey[1]

  • [1] University of Michigan Department of Mathematics 2074 East Hall 530 Church Street Ann Arbor, MI 48109-1043 (USA)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 3, page 599-624
  • ISSN: 0373-0956

Abstract

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In this paper we introduce a geometric formalism for studying modular forms of half-integral weight. We then use this formalism to define p -adic modular forms of half-integral weight and to construct p -adic Hecke operators.

How to cite

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Ramsey, Nick. "Geometric and $p$-adic Modular Forms of Half-Integral Weight." Annales de l’institut Fourier 56.3 (2006): 599-624. <http://eudml.org/doc/10159>.

@article{Ramsey2006,
abstract = {In this paper we introduce a geometric formalism for studying modular forms of half-integral weight. We then use this formalism to define $p$-adic modular forms of half-integral weight and to construct $p$-adic Hecke operators.},
affiliation = {University of Michigan Department of Mathematics 2074 East Hall 530 Church Street Ann Arbor, MI 48109-1043 (USA)},
author = {Ramsey, Nick},
journal = {Annales de l’institut Fourier},
keywords = {Modular forms of half-integral weight; $p$-adic modular forms; modular forms of half-integral weight; -adic modular forms; Hecke operators; modular curves; -expansion principle},
language = {eng},
number = {3},
pages = {599-624},
publisher = {Association des Annales de l’institut Fourier},
title = {Geometric and $p$-adic Modular Forms of Half-Integral Weight},
url = {http://eudml.org/doc/10159},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Ramsey, Nick
TI - Geometric and $p$-adic Modular Forms of Half-Integral Weight
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 3
SP - 599
EP - 624
AB - In this paper we introduce a geometric formalism for studying modular forms of half-integral weight. We then use this formalism to define $p$-adic modular forms of half-integral weight and to construct $p$-adic Hecke operators.
LA - eng
KW - Modular forms of half-integral weight; $p$-adic modular forms; modular forms of half-integral weight; -adic modular forms; Hecke operators; modular curves; -expansion principle
UR - http://eudml.org/doc/10159
ER -

References

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  1. Kevin Buzzard, Analytic continuation of overconvergent eigenforms, J. Amer. Math. Soc. 16 (2003), 29-55 Zbl1076.11029MR1937198
  2. R. Coleman, B. Mazur, The eigencurve, Galois representations in arithmetic algebraic geometry (Durham, 1996) 254 (1998), 1-113, Cambridge Univ. Press, Cambridge Zbl0932.11030MR1696485
  3. Robert F. Coleman, p -adic Banach spaces and families of modular forms, Invent. Math. 127 (1997), 417-479 Zbl0918.11026MR1431135
  4. Nicholas M. Katz, p -adic properties of modular schemes and modular forms, Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) 350 (1973), 69-190, Springer, Berlin Zbl0271.10033MR447119
  5. Nicholas M. Katz, Barry Mazur, Arithmetic moduli of elliptic curves, 108 (1985), Princeton University Press, Princeton, NJ Zbl0576.14026MR772569
  6. Nicholas Ramsey, The half-integral weight eigencurve Zbl1191.11011
  7. Nicholas Ramsey, Geometric and p -adic Modular Forms of Half-Integral Weight, (2004) 
  8. Goro Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440-481 Zbl0266.10022MR332663

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