On the Fourier coefficients of modular forms

Douglas L. Ulmer

Annales scientifiques de l'École Normale Supérieure (1995)

  • Volume: 28, Issue: 2, page 129-160
  • ISSN: 0012-9593

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Ulmer, Douglas L.. "On the Fourier coefficients of modular forms." Annales scientifiques de l'École Normale Supérieure 28.2 (1995): 129-160. <http://eudml.org/doc/82380>.

@article{Ulmer1995,
author = {Ulmer, Douglas L.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {modular form; Fourier coefficients; Hodge polygon; Newton polygon; log scheme; Newton-Hodge inequality},
language = {eng},
number = {2},
pages = {129-160},
publisher = {Elsevier},
title = {On the Fourier coefficients of modular forms},
url = {http://eudml.org/doc/82380},
volume = {28},
year = {1995},
}

TY - JOUR
AU - Ulmer, Douglas L.
TI - On the Fourier coefficients of modular forms
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1995
PB - Elsevier
VL - 28
IS - 2
SP - 129
EP - 160
LA - eng
KW - modular form; Fourier coefficients; Hodge polygon; Newton polygon; log scheme; Newton-Hodge inequality
UR - http://eudml.org/doc/82380
ER -

References

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  1. [BO] P. BERTHELOT and A. OGUS, Notes on Crystalline Cohomology, Princeton University Press, 1978. Zbl0383.14010MR58 #10908
  2. [CO] H. COHEN and J. OESTERLÉ, Dimensions des espaces de formes modulaires in : J.-P. Serre and D.B. Zagier, Eds. Modular Functions of One Variable VI, (Lect. Notes in Math., Vol. 627, 1977, pp. 69-73). Zbl0371.10020MR57 #12396
  3. [D1] P. DELIGNE, Formes modulaire et représentations ℓ-adiques (Séminaire Bourbaki 1968-1969, Lect. Notes in Math., Vol. 179, 1969, pp. 139-172). Zbl0206.49901
  4. [D2] P. DELIGNE, Théorie de Hodge, II (Inst. Hautes Études Sci. Publ. Math., Vol. 40, 1972, pp. 5-57). Zbl0219.14007
  5. [H] R. HARTSHORNE, Algebraic Geometry, Berlin Heidelberg New York, Springer, 1977. Zbl0367.14001MR57 #3116
  6. [Ig] J.-I. IGUSA, On the algebraic theory of elliptic modular functions (J. Math. Soc. Japan, Vol. 20, 1968, pp. 96-106). Zbl0164.21101MR39 #1457
  7. [I] L. ILLUSIE, Complexe de de Rham-Witt et cohomologie cristalline (Ann. Sci. Éc. Norm. Sup., Vol. 12, 1979, pp. 501-661). Zbl0436.14007MR82d:14013
  8. [Ko] K. KATO, Logarithmic structures of Fontaine-Illusie in : J.-I. Igusa, Ed. Algebraic Analysis, Geometry and Number Theory (Proceedings of the JAMI inaugural conference, 1989, pp. 191-224). Zbl0776.14004MR99b:14020
  9. [K1] N. KATZ, Slope Filtration of F-crystals (Astérisque, Vol. 63, 1979, pp. 113-164). Zbl0426.14007MR81i:14014
  10. [K2] N. KATZ, p-adic properties of modular schemes and modular forms in : W. Kuyk and J.-P. Serre, Ed. Modular Functions of One Variable III (Lect. Notes in Math., Vol. 350, 1973, pp. 69-190). Zbl0271.10033MR56 #5434
  11. [KM] N. KATZ and B. MAZUR, Arithmetic Moduli of Elliptic Curves, Princeton University Press, 1985. Zbl0576.14026MR86i:11024
  12. [KMe] N. KATZ and W. MESSING, Some consequences of the Riemann hypothesis for varieties over finite fields (Invent. Math., Vol. 23, 1974, pp. 73-77). Zbl0275.14011MR48 #11117
  13. [KKMS] G. KEMPF, F. KNUDSEN, D. MUMFORD and B. SAINT-DONAT, Toroidal Embeddings I (Lect. Notes in Math., Vol. 339, 1973). Zbl0271.14017MR49 #299
  14. [Ma] B. MAZUR, Frobenius and the Hodge filtration (Bull. Amer. Math. Soc., Vol. 78, 1972, pp. 653-667). Zbl0258.14006MR48 #8507
  15. [M1] J. S. MILNE, On a conjecture of Artin and Tate (Annals of Math., (2), Vol. 102, 1975, pp. 517-533). Zbl0343.14005MR54 #2659
  16. [M2] J. S. MILNE, Etale Cohomology, Princeton University Press, 1980. Zbl0433.14012MR81j:14002
  17. [Mi] T. MIYAKE, Modular Forms, Berlin Heidelberg New York, Springer, 1989. Zbl0701.11014MR90m:11062
  18. [N] N. Nygaard, Slopes of powers of Frobenius on crystalline cohomology (Ann. Sci. Éc. Norm. Sup., Vol. 14, 1981, pp. 369-401). Zbl0519.14012MR84d:14011
  19. [O] T. ODA, Convex Bodies and Algebraic Geometry, Berlin Heidelberg New York, Springer, 1985. 
  20. [S] A. J. SCHOLL, Motives for modular forms (Invent. Math., Vol. 100, 1990, pp. 419-430). Zbl0760.14002MR91e:11054
  21. [U1] D. L. ULMER, On universal elliptic curves over Igusa curves (Invent. Math., Vol. 99, 1990, pp. 377-391). Zbl0705.14024MR90m:11092
  22. [U2] D. L. ULMER, L-functions of universal elliptic curves over Igusa curves (Amer. J. Math., Vol. 112, 1990, pp. 687-712). Zbl0731.14013MR91j:11050

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