# 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

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topRamsey, 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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- Robert F. Coleman, $p$-adic Banach spaces and families of modular forms, Invent. Math. 127 (1997), 417-479 Zbl0918.11026MR1431135
- 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
- Nicholas M. Katz, Barry Mazur, Arithmetic moduli of elliptic curves, 108 (1985), Princeton University Press, Princeton, NJ Zbl0576.14026MR772569
- Nicholas Ramsey, The half-integral weight eigencurve Zbl1191.11011
- Nicholas Ramsey, Geometric and $p$-adic Modular Forms of Half-Integral Weight, (2004)
- Goro Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440-481 Zbl0266.10022MR332663

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