Advertisement

Waldspurger’s Formula and Central Critical Values of L-Functions of Newforms in Weight Aspect

  • Winfried Kohnen
  • Jyoti Sengupta
Part of the Developments in Mathematics book series (DEVM, volume 8)

Abstract

We shall give a proof of the Lindelöf hypothesis in weight aspect on the average for central critical values of quadratic character twists of Hecke L-functions attached to cuspidal Hecke eigenforms. One of the basic tools will be Waldspurger’s results on central critical values of L-functions in weight aspect.

Keywords

Waldspurger’s formula Jacobi form Lindelöf hypothesis Poincaré series 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. Eichler and D. Zagier, The theory of Jacobi forms, Progress in Math. vol. 55, Birkhäuser: Boston 1985Google Scholar
  2. [2]
    B. Gross, W. Kohnen and D. Zagier, Heegner points and derivatives of L-series. II, Math. Ann. 278, 497–562 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    H. Iwaniec, Small eigenvalues of Laplacian for Γ0(N), Acta Arith. 56, 65–82 (1990)MathSciNetzbMATHGoogle Scholar
  4. [4]
    H. Iwaniec and P. Michel, The second moment of the symmetric square L-functions, Ann. Acad. Sci. Fennicae 26, 465–482 (2001)MathSciNetzbMATHGoogle Scholar
  5. [5]
    W. Kohnen and J. Sengupta, On quadratic character twists of Hecke L-functions attached to cusp forms of varying weights at the central point, Acta Arith. 99, 61–66 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    N.-P. Skoruppa and D. Zagier, Jacobi forms and a certain space of modular forms, Invent. math. 94, 113–146 (1988)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Winfried Kohnen
    • 1
  • Jyoti Sengupta
    • 2
  1. 1.Mathematisches InstitutUniversität HeidelbergHeidelbergGermany
  2. 2.Jyoti Sengupta, T.I.F.R.School of MathematicsBombayIndia

Personalised recommendations