Skip to main content
SpringerLink
Log in

The critical order of vanishing of automorphicL-functions with large level

  • Published:
Inventiones mathematicae Aims and scope

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. S. Böcherer, R. Schulze-Pillot: The Dirichlet series of Koecher and Maass and modular forms of weight 3/2. Math. Z.209 (1992) 273–287

    Google Scholar 

  2. J.-M. Deshouillers, H. Iwaniec: Kloosterman sums and Fourier coefficients of cusp forms. Invent. Math.70 (1982) 219–288

    Google Scholar 

  3. W. Duke, J. Friedlander, H. Iwaniec: Bounds for automorphicL-functions. II. Invent. Math.115 (1994) 219–239

    Google Scholar 

  4. D. Goldfeld, J. Hoffstein, D. Lieman: An effective zero free region, Appendix to: Coefficeints of Maass forms and the Siegel zero Ann. Math. (to appear)

  5. F. Gouvêa, B. Mazur: The square-free sieve and the rank of elliptic curves. J. AMS4 (1991) 1–23

    Google Scholar 

  6. B.H. Gross: Heights and the special values ofL-series. In: Number Theory, Proceedings of the 1985 Montreal Conference held June 17–29, 1985, CMS Conference Proceedings, Vol. 7, 1987, 115–187

  7. J. Hoffstein, P. Lockhart: Coefficients of Maass forms and the Siegel zero. Ann. Math. (to appear)

  8. H. Iwaniec: On the order of vanishing of modularL-functions at the critical point. In: Sém. Th. des Nombres, Bordeaux2 (1990) 365–376

  9. W. Luo: On the nonvanishing of Rankin SelbergL-functions. Duke Math. J69 (1993) 411–427

    Google Scholar 

  10. B. Mazur: Modular curves and the Eisenstein ideal. IHES Publ. Math.47 (1977) 33–186

    Google Scholar 

  11. B. Mazur: On the arithmetic of special values ofL-functions. Invent. Math.55 (1979) 207–240

    Google Scholar 

  12. D.E. Rohrlich: OnL-functions of elliptic curves and cyclotomic towers. Invent. Math.75 (1984) 409–423

    Google Scholar 

  13. D.E. Rohrlich:L-functions and division towers. Math. Ann.281 (1988) 611–632

    Google Scholar 

  14. G. Shimura: Introduction to the arithmetic theory of automorphic functions. Publ. Math. Soc. Japan, Vol. 11. Tokyo-Princeton, 1971

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    W. Duke

Authors
  1. W. Duke
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Oblatum 19-IX-1993 & 2-V-1994

Research supported in part by NSF Grant DMS-9202022.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Duke, W. The critical order of vanishing of automorphicL-functions with large level. Invent Math 119, 165–174 (1995). https://doi.org/10.1007/BF01245178

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01245178

Keywords

Search

Navigation