Mathematische Annalen

, Volume 212, Issue 4, pp 285–315 | Cite as

Newforms and functional equations

  • Wen-Ch'ing Winnie Li
Article

Keywords

Functional Equation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atkin, A., Lehner, J.: Hecke operators on Γ0(m). Math. Ann.185, 134–160 (1970)Google Scholar
  2. 2.
    Casselman, W.: On some results of Atkin and Lehner. Math. Ann.201, 301–314 (1973)Google Scholar
  3. 3.
    Hecke, E.: Mathematische Werke. Göttingen: Vandenhoeck und Ruprecht 1959Google Scholar
  4. 4.
    Jacquet, H.: Automorphic forms on GL (2), Part II. Springer Lecture Notes, No.278 (1972)Google Scholar
  5. 5.
    Mazur, B.: Courbes elliptiques et symboles modulaires. Séminaire Bourbaki, 24e année, 1971/72; n0 414Google Scholar
  6. 6.
    Miyake, T.: On automorphic forms on GL2 and Hecke operators. Annals of Math.94, 174–189 (1971)Google Scholar
  7. 7.
    Ogg, A.: On the eigenvalues of Hecke operators. Math. Ann.179, 101–108 (1969)Google Scholar
  8. 8.
    Ogg, A.: On a convolution ofL-series. Inventiones math.7, 297–312 (1969)Google Scholar
  9. 9.
    Petersson, H.: Konstruktion der sämtlichen Lösungen einer Riemannschen Funktionalgleichung durch Dirichlet-Reihen mit Eulerscher Produktentwicklung, I, II, III. Math. Ann.116, 401–412 (1939), and117, 39–64 and 277–300 (1940–1941)Google Scholar
  10. 10.
    Rankin, R.: Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions. II. Proc. Camb. Phil. Soc.35, 357–372 (1939)Google Scholar
  11. 11.
    Selberg, A.: On the estimation of Fourier coefficients of modular forms. Proc. Symposium Pure Math. (Amer. Math. Soc.) VIII, 1–15 (1965)Google Scholar
  12. 12.
    Serre, J.: Formes modulaires et fonctions zêtap-adiques. Summer School on Modular Functions, Antwerp (1972). Springer Lecture Notes, No.350, 191–268, Berlin-Heidelberg-New York: Springer 1972Google Scholar
  13. 13.
    Serre, J.: Facteurs locaux des fonctions zêta des variétés algébriques. Séminaire Delange-Pisot-Poitou (Théorie des Nombres), 11e année, 1969/70, n0 19Google Scholar
  14. 14.
    Shimura, G.: On modular forms of half integral weight. Annals of Math.97, 440–481 (1973)Google Scholar
  15. 15.
    Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Math. Soc. Japan11 (1971), Princeton Univ. PressGoogle Scholar
  16. 16.
    Weil, A.: Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen. Math. Ann.168, 149–156 (1967)Google Scholar
  17. 17.
    Weil, A.: Dirichlet series and automorphic forms. Springer Lecture Notes, No.189. Berlin-Heidelberg-New York: Springer 1971Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Wen-Ch'ing Winnie Li
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

Personalised recommendations