Skip to main content
SpringerLink
Log in

Modular forms whose fourier coefficients involve zeta-functions of quadratic fields

  • Conference paper
  • First Online:
Modular Functions of One Variable VI

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 627))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
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. T. Asai, On the Fourier coefficients of automorphic forms at various cusps and some applications to Rankin's convolution, J. Math. Soc. Japan 28 (1976) 48–61

    Article  MathSciNet  MATH  Google Scholar 

  2. T. Asai, On certain Dirichlet series associated with Hilbert modular forms and Rankin's method, Math. Ann. 226 (1977) 81–94.

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Cohen, Sums involving the values at negative integers of L functions of quadratic characters, Math. Ann. 217 (1975) 271–285.

    Article  MathSciNet  MATH  Google Scholar 

  4. K. Doi, H. Naganuma, On the functional equation of certain Dirichlet series, Inv. Math. 9 (1969) 1–14

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Erdelyi, W. Magnus, F. Oberhettinger, F. Tricomi, Higher Transcendental Functions, Vol. I, Mc Graw-Hill, New York-Toronto-London 1953.

    MATH  Google Scholar 

  6. R. Gunning, Lectures on Modular Forms, Ann. of Math. Studies No. 48, Princeton Univ. Press, Princeton 1962.

    Book  MATH  Google Scholar 

  7. F. Hirzebruch, Kurven auf den Hilbertschen Modulflächen und Klassenzahl-relationen, in Classification of algebraic varieties and compact complex manifolds, Springer Lecture Notes No. 412, pp. 75–93.

    Google Scholar 

  8. F. Hirzebruch, D. Zagier, Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus, Inv. Math. 36 (1976) 57–113

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Hurwitz, Über Relationen zwischen Klassenzahlen binärer quadratischer Formen von negativer Determinante, Math. Ann. 25 (1885). Math. Werke, Bd. II, pp. 8–50, Birkhäuser, Basel-Stuttgart 1963

    Google Scholar 

  10. E. Landau, Vorlesungen über Zahlentheorie (Aus der elementaren Zahlentheorie), Hirzel, Leipzig 1927.

    MATH  Google Scholar 

  11. S. Lang, Introduction to Modular Forms, Grundlehren der mathematischen Wissenschaften 222, Springer-Verlag, Berlin-Heidelberg-New York 1976

    MATH  Google Scholar 

  12. D.H. Lehmer, Ramanujan's function τ(n), Duke Math. J. 10 (1943) 483–492.

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Li, New forms and functional equations, Math. Ann 212 (1975) 285–315.

    Article  MathSciNet  Google Scholar 

  14. H. Naganuma, On the coincidence of two Dirichlet series associated with cusp forms of Hecke's “Neben”-type and Hilbert modular forms over a real quadratic field, J. Math. Soc. Japan 25 (1973) 547–555.

    Article  MathSciNet  MATH  Google Scholar 

  15. T. Oda, On modular forms associated with indefinite quadratic forms of signature (2, n-2), Math. Ann., to appear

    Google Scholar 

  16. H. Petersson, Über eine Metrisierung der ganzen Modulformen, Jahresb. d. Deutschen Math. Verein. 49 (1939) 49–75.

    MATH  Google Scholar 

  17. R. A. Rankin, Contributions to the theory of Ramanujan's function τ(n) and similar arithetical functions, I, Proc. Camb. Phil. Soc. 35 (1939) 351–372.

    Article  MathSciNet  Google Scholar 

  18. R.A. Rankin, The scalar product of modular forms, Proc. London Math. Soc. 2 (1952) 198–217

    Article  MathSciNet  MATH  Google Scholar 

  19. J-P. Serre, Une interprétation des congruences relatives à la fonction τ de Ramanujan, Séminaire Delange-Pisot-Poitou, 9e année, 1967/8, no 14

    Google Scholar 

  20. G. Shimura, On modular forms of half integral weight, Ann of Math. 97 (1973) 440–481

    Article  MathSciNet  MATH  Google Scholar 

  21. G. Shimura, On the holomorphy of certain Dirichlet series, Proc. Lond. Math. Soc. 31 (1975) 79–98

    Article  MathSciNet  MATH  Google Scholar 

  22. G. Shimura, The special values of the zeta functions associated with cusp forms, Comm. on Pure and Applied Math. 29 (1976) 783–804

    Article  MathSciNet  MATH  Google Scholar 

  23. D. Zagier, On the values at negative integers of the zeta-function of a real quadratic field, L'Ens. Math. 22 (1976) 55–95.

    MathSciNet  MATH  Google Scholar 

  24. D. Zagier, Modular forms associated to real quadratic fields, Inv. Math. 30 (1975) 1–46

    Article  MathSciNet  MATH  Google Scholar 

  25. D. Zagier, Traces des opérateurs de Hecke, Séminaire Delange-Pisot-Poitou, 17e année, 1975/6, no 23; = The Eichler-Selberg trace formula on SL2(Z), Appendix to Part I of [11], pp. 44–54.

    Google Scholar 

Download references

Authors
  1. D. Zagier
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jean-Pierre Serre Don Bernard Zagier

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Springer-Verlag

About this paper

Cite this paper

Zagier, D. (1977). Modular forms whose fourier coefficients involve zeta-functions of quadratic fields. In: Serre, JP., Zagier, D.B. (eds) Modular Functions of One Variable VI. Lecture Notes in Mathematics, vol 627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065299

Download citation

  • DOI: https://doi.org/10.1007/BFb0065299

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08530-0

  • Online ISBN: 978-3-540-35984-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation