Inventiones mathematicae

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

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



Large Level Critical Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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