Skip to main content
SpringerLink
Log in

L-series of Rankin type and their functional equations

  • 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. Atkin, A., Lehner, J.: Hecke operators on Γ0(m), Math. Ann.185, 134–160 (1970)

    Google Scholar 

  2. Atkin, A., Li, W.: Twists of newforms and pseudo-eigenvalues ofW-operators. Invent. Math.48, 221–243 (1978)

    Google Scholar 

  3. Deligne, P.: Formes modulaires et représentations de GL(2). In: Modular functions of one variable. II. Lecture Notes in Mathematics, Vol.349, pp. 55–105. Kuyk, W., Deligne, P. (eds.) Berlin, Heidelberg, New York: Springer 1973

    Google Scholar 

  4. Gelbart, S., Jacquet, H.: A relation between automorphic representations of GL(2) and GL(3). Ann. Sci. École Norm. Sup. (4e),11 (1978)

  5. Jacquet, H.: Automorphic forms on GL(2). Part II. Lecture Notes in Mathematics, Vol.278, Berlin, Heidelberg, New York: Springer 1972

    Google Scholar 

  6. Jacquet, H., Langlands, R.: Automorphic forms on GL(2). Lecture Notes in Mathematics, Vol.114. Berlin, Heidelberg, New York: Springer 1970

    Google Scholar 

  7. Li, W.: On the representations of GL(2). Part I. ɛ-factors andn-closeness, J. reine angew. Math. (to appear)

  8. Li, W.: Newforms and functional equations, Math. Ann.212, 285–315 (1975)

    Google Scholar 

  9. Manin, J., Panchishkin, A.: Convolution of Hecke series and their values at integral points. Math. Sbornik104 (146), No. 4 (12), 617–651 (1977) (in Russian)

    Google Scholar 

  10. Ogg, A.: On a convolution ofL-series. Invent. Math.7, 297–312 (1969)

    Google Scholar 

  11. Petersson, H.: Über die Berechnung der Skalarprodukte ganzer Modulformen. Comment. Math. Helv.22, 168–199 (1949)

    Google Scholar 

  12. 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 

  13. Selberg, A.: Bemerkungen über eine Dirichletsche Reihe die mit der Theorie der Modulformen nahe verbunden ist. Arch. Math. Naturvid43, 47–50 (1940)

    Google Scholar 

  14. Serre, J.-P.: Facteurs locaux des functions zêta des variétés algébriques (définitions et conjectures). Séminaire Delange-Pisot-Poitou (Théorie de Nombres) 11e année no 19 (1969/70)

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

    Google Scholar 

  16. Tate, J.: Local constants, algebraic number fields (L-functions and Galois properties). A. Fröhlich (ed.), pp. 89–131. London, New York: Academic Press 1977

    Google Scholar 

  17. Zagier, D.: Modular forms whose Fourier coefficients involve zeta functions of quadratic fields, modular functions of one variable. VI. Lecture Notes in Mathematics, Vol.627. Serre, J.P., Zagier, D.B. (eds.), Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Institute for Advanced Study, 08540, Princeton, NJ, USA

    Wen-Ch'ing Winnie Li

  2. Harvard University Cambridge, 02138, MA, USA

    Wen-Ch'ing Winnie Li

Authors
  1. Wen-Ch'ing Winnie Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by the NSF grant no. MCS73-08412

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, WC.W. L-series of Rankin type and their functional equations. Math. Ann. 244, 135–166 (1979). https://doi.org/10.1007/BF01420487

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01420487

Keywords

Search

Navigation