Inventiones mathematicae

, Volume 119, Issue 1, pp 165–174 | Cite as

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

Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Böcherer, R. Schulze-Pillot: The Dirichlet series of Koecher and Maass and modular forms of weight 3/2. Math. Z.209 (1992) 273–287Google Scholar
  2. 2.
    J.-M. Deshouillers, H. Iwaniec: Kloosterman sums and Fourier coefficients of cusp forms. Invent. Math.70 (1982) 219–288Google Scholar
  3. 3.
    W. Duke, J. Friedlander, H. Iwaniec: Bounds for automorphicL-functions. II. Invent. Math.115 (1994) 219–239Google Scholar
  4. 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)Google Scholar
  5. 5.
    F. Gouvêa, B. Mazur: The square-free sieve and the rank of elliptic curves. J. AMS4 (1991) 1–23Google Scholar
  6. 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, 115–187Google Scholar
  7. 7.
    J. Hoffstein, P. Lockhart: Coefficients of Maass forms and the Siegel zero. Ann. Math. (to appear)Google Scholar
  8. 8.
    H. Iwaniec: On the order of vanishing of modularL-functions at the critical point. In: Sém. Th. des Nombres, Bordeaux2 (1990) 365–376Google Scholar
  9. 9.
    W. Luo: On the nonvanishing of Rankin SelbergL-functions. Duke Math. J69 (1993) 411–427Google Scholar
  10. 10.
    B. Mazur: Modular curves and the Eisenstein ideal. IHES Publ. Math.47 (1977) 33–186Google Scholar
  11. 11.
    B. Mazur: On the arithmetic of special values ofL-functions. Invent. Math.55 (1979) 207–240Google Scholar
  12. 12.
    D.E. Rohrlich: OnL-functions of elliptic curves and cyclotomic towers. Invent. Math.75 (1984) 409–423Google Scholar
  13. 13.
    D.E. Rohrlich:L-functions and division towers. Math. Ann.281 (1988) 611–632Google Scholar
  14. 14.
    G. Shimura: Introduction to the arithmetic theory of automorphic functions. Publ. Math. Soc. Japan, Vol. 11. Tokyo-Princeton, 1971Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • W. Duke
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

Personalised recommendations