Skip to main content
SpringerLink
Log in

On certain Dirichlet series associated with automorphic forms on SL(2,C)

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

In this note, we will discuss the analogy of some results of Asai [2] in the case of the automorphic forms on SL(2,C). Being combined with the base change lifting to the imaginary quadratic field, we will discuss the L-function L(s,f,Sym2) for an elliptic modular form f. The base change lifting to the field of higher degree will also be discussed.

The author would like to express his hearty thanks to Prof. Nobushige Kurokawa for his valuable suggestions on the meromorphy of Euler products.

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

Similar content being viewed by others

References

  1. Asai,T.: On the Fourier coefficients of automorphic forms at various cusps and applications to Rankin convolution. J. Math. Soc. Japan 28 (1976) 48–61

    Google Scholar 

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

    Google Scholar 

  3. Asai,T.: On the Doi-Naganuma lifting associated with imaginary quadratic fields. Nagoya Math.J. 71 (1978) 149–167

    Google Scholar 

  4. Deligne,P.: La conjecture de Weil I. Publ.Math. I.H.E.S. 43 (1974) 273–307

    Google Scholar 

  5. Deligne.P. and Serre,J.-P.: Formes modulaires de poids 1. Ann.Sci. Ecole Norm.Sup. (4) 7 (1974) 507–530

    Google Scholar 

  6. Kurokawa,N.: On some Euler products I, II. Proc.Japan Acad. vol.60 Ser.A, No.9 (1984) 335–338. ibid. No. 10 (1984) 365–368

    Google Scholar 

  7. Kurokawa,N.: On the meromorphy of Euler products I, II. Proc. London Math.Soc. 53 (1986) (in press)

  8. Langlands,R.P.: Euler products. Yale Univ. (1971)

  9. Langlands,R.P.: Base change for GL(2), the theory of Saito-Shintani with applications. Institute for Advanced Study, Princeton, N.J. (1975)

    Google Scholar 

  10. Langlands,R.P.: Automorphic representations, Shimura varieties, and motives. Ein Märchen Proc.Sympos.Pure Math. vol.33 part 2. Amer.Math.Soc. Providence, R.I. (1979) 205–246

    Google Scholar 

  11. Takase,K.: On the wave forms on 0(1,q+1) and the associated Dirichlet series. (preprint)

  12. Tate,J.: Number theoretic background. Proc.Sympos.Pure Math. vol.33 part 2, Amer.Math.Soc. Providence, R.I. (1979) 3–26

    Google Scholar 

  13. Weil,A.: Dirichlet series and automorphic forms. Lecture Notes in Math. 189 (1971) Springer-Verlag

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Tokyo Institute of Technology, Oh-Okayama, Meguro-Ku, 152, Tokyo, Japan

    Koichi Takase

Authors
  1. Koichi Takase
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Takase, K. On certain Dirichlet series associated with automorphic forms on SL(2,C). Manuscripta Math 56, 293–312 (1986). https://doi.org/10.1007/BF01180770

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01180770

Keywords

Search

Navigation