Skip to main content
SpringerLink
Log in

On the Fourier coefficients of modular forms. II

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Ekedahl, T.: Diagonal complexes and F-gauge structures. Paris: Hermann (Travaux en cours 18) 1986

    Google Scholar 

  2. Hida, H.: Galois representations into GL2(ℤ p [[X]]) attached to ordinary cusp forms. Invent. Math.85 (1986) 545–613

    Google Scholar 

  3. Illusie, L.: Complexe de deRham-Witt et cohomologie cristalline. Ann. Sci. Ec. Norm. Supér. (4)12 (1979) 501–661

    Google Scholar 

  4. Illusie, L.: Finiteness, duality, and Künneth theorems in the cohomology of the deRham Witt complex. In: Raynaud, M. and Shiota, T. (eds.) Algebraic Geometry Tokyo-Kyoto (Lect. Notes in Math. 1016.) pp. 20–72 Berlin Heidelberg New York: Springer 1982

    Google Scholar 

  5. Illusie, L. and Raynaud, M.: Les suites spectrales associées au complexe de deRham-Witt Inst. Hautes Etudes Sci. Publ. Math.57 (1983) 73–212

    Google Scholar 

  6. Katz, N.:p-adic properties of modular schemes and modular forms. In: Kuyk, W. and Serre, J.-P. (Eds.) Modular Functions of One Variable II (Lect. Notes in Math. 350). pp. 69–190 Berlin Heidelberg New York: Springer 1973

    Google Scholar 

  7. Katz, N.: A result on modular forms in characteristicp. In: Serre, J.-P. and Zagier, D.B. (Eds.) Modular Functions of One Variable V (Lect. Notes in Math. 601.) pp. 53–61 Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  8. Katz, N.: Slope filtration of F-crystals. Astérisque63 (1979) 113–164

    Google Scholar 

  9. Katz, N. and Mazur, B.: Arithmetic Moduli of Elliptic Curves. Princeton: Princeton University Press 1985

    Google Scholar 

  10. Katz, N. and Oda, T.: On the differentiation of deRham cohomology classes with respect to parameters. J. Math. Kyoto Univ.8 (1968) 199–213

    Google Scholar 

  11. Milne, J.S.: Values of zeta functions of varieties over finite fields. Amer. J. Math.108 (1986) 297–360

    Google Scholar 

  12. Miyake, T.: Modular Forms, Berlin Heidelberg New York: Springer 1989

    Google Scholar 

  13. Oda, T.: The first deRham cohomology group and Dieudonné modules. Ann. Sci. Ec. Norm. Supér. (4)2 (1969) 63–135

    Google Scholar 

  14. Serre, J.-P.: Groupes Algebriques et Corps de Classes. Paris: Hermann 1959

    Google Scholar 

  15. Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions. Princeton: Princeton University Press 1971

    Google Scholar 

  16. Ulmer, D.L.:p-descent in characteristicp. Duke Math. J.62 (1991) 237–265

    Google Scholar 

  17. Ulmer, D.L.: On the Fourier coefficients of modular forms. Ann. Sci. Ec. Norm. Supér. (4)28 (1995) 129–160

    Google Scholar 

  18. Ulmer, D.L.: Slopes of modular forms. In: Childress, N. and Jones, J. (eds.) Arithmetic Geometry (Contemp. Math.174) (1994) 167–183

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Arizona, 85721, Tucson, AZ, USA

    Douglas L. Ulmer

Authors
  1. Douglas L. Ulmer
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was partially supported by NSF grant DMS 9114816

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ulmer, D.L. On the Fourier coefficients of modular forms. II. Math. Ann. 304, 363–422 (1996). https://doi.org/10.1007/BF01446299

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01446299

Mathematics Subject Classification (1991)

Search

Navigation