Skip to main content

Universal Fourier expansions of modular forms

  • Chapter
  • First Online:
On Artin's Conjecture for Odd 2-dimensional Representations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1585))

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gross B., Zagier D. Heegner points and derivatives of L-series. Inv. Math., 84:225–320, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  2. Heilbronn H. On the average length of a class of continued fractions. In Paul Turan, editor, Abhandlungen aus Zahlentheorie und analysis zur Errinerung an Edmund Landau, pages 88–96. VEB Deutscher Verlag der Wissenschaften, Berlin, 1969.

    Google Scholar 

  3. Lang S.Introduction to modular forms. Number 222 in Grundlehren der Mathematischen Wissenschaften. Springer Verlag, 1976.

    Google Scholar 

  4. Manin Y. Parabolic points and zeta function of modular curves. Math. USSR Izvestija 6 (1): 19–64, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  5. Manin Y. Explicit formulas for the eigenvalues of Hecke operators. Acta arithmetica, XXIV:?, 1973.

    Google Scholar 

  6. Manin Y. Periods of parabolic forms and p-adic Hecke series. Math. USSR Sbornik, 21:371–393, 1973.

    Article  MATH  Google Scholar 

  7. Merel L. Opérateurs de Hecke et sous-groupes de Γ(2). Journal of Number theory. To appear, (=Thèse, chapitre 5).

    Google Scholar 

  8. Merel L. Opérateurs de Hecke pour Γ0(N) et fractions continues. Ann. Inst. Fourier, 41(3), 1991. (=thèse, chapitre 2).

    Google Scholar 

    Google Scholar 

  9. Merel L. Homologie des courbes modulaires affines et paramétrisations de Weil. 1992. To appear, (=Thèse, chapitre 3).

    Google Scholar 

  10. Serre J-P. Cours d'arithmétique. Presses Universitaires de France, 1970.

    Google Scholar 

  11. Shokurov V. Holomorphic differential forms of higher degree on Kuga's modular varieties. Math. USSR Sbornik, 30 (1): 119–142, 1976.

    Article  Google Scholar 

  12. Shokurov V. Modular symbols of arbitrary weight. Functional analysis and its applications, 10 (1): 85–86, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  13. Shokurov V. Shimura integrals of cusp forms. Math. USSR Isvestija, 16 (3): 603–646, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  14. Shokurov V. The study of the homology of Kuga varieties. Math. USSR Isvestija, 16 (2): 399–418, 1981.

    Article  MATH  Google Scholar 

  15. Wang X. This volume.

    Google Scholar 

  16. Zagier D. Hecke operators and periods of modular forms. Israel Mathematical Conference Proceedings, 3:321–336, 1990.

    MathSciNet  MATH  Google Scholar 

  17. Zagier D. Periods of modular forms and jacobi theta functions. Invent. Math., 104(3): 449–465, 1991. *** DIRECT SUPPORT *** A00I6B42 00003

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Gerhard Frey

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag

About this chapter

Cite this chapter

Merel, L. (1994). Universal Fourier expansions of modular forms. In: Frey, G. (eds) On Artin's Conjecture for Odd 2-dimensional Representations. Lecture Notes in Mathematics, vol 1585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074110

Download citation

  • DOI: https://doi.org/10.1007/BFb0074110

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58387-5

  • Online ISBN: 978-3-540-48681-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics