Archiv der Mathematik

, Volume 97, Issue 6, pp 535–547 | Cite as

The sixth moment of the family of Γ1(q)-automorphic L-functions

  • Goran Djanković


In this paper we investigate the sixth moment of the family of L-functions associated to holomorphic modular forms on GL 2 with respect to a congruence subgroup Γ1(q). The bound for central values averaged over the family, consistent with the Lindelöf hypothesis, is obtained for prime levels q.

Mathematics Subject Classification (2010)

11M41 11F11 11F67 


Automorphic forms L-functions Moments 


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  1. 1.
    J. B. Conrey, H. Iwaniec, and K. Soundararajan, The sixth power moment of Dirichlet L-functions, arXiv: 0710.5176v1Google Scholar
  2. 2.
    Huxley M.N.: The large sieve inequality for algebraic number fields II. Means of moments of Hecke zeta-functions. Proc. London Math. Soc. 21, 108–128 (1970)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    A. Ivić, On the Ternary Additive Divisor Problem and the Sixth Moment of the Zeta-Function, in Sieve Methods, Exponential Sums, and their Applications in Number Theory, London Math. Soc. Lecture Note Series 237, 205–243, Cambridge Univ. Press, Cambridge, 1997.Google Scholar
  4. 4.
    H. Iwaniec, Automorphic Number Theory, Current Developments in Mathematics, 2003, 35–52.Google Scholar
  5. 5.
    H. Iwaniec, Topics in Classical Automorphic Forms, Graduate Studies in Mathematics, 17, American Mathematical Society, Providence, RI, 1997.Google Scholar
  6. 6.
    H. Iwaniec and E. Kowalski, Analytic Number Theory, American Mathematical Society Colloquium Publications 53, AMS, Providence, 2004.Google Scholar
  7. 7.
    Iwaniec H., Li X.: The orthogonality of Hecke eigenvalues. Compositio Math. 143, 541–565 (2007)MATHMathSciNetGoogle Scholar
  8. 8.
    S. D. Miller and W. Schmid, Summation formulas, from Poisson and Voronoi to the present, Noncommutative harmonic analysis, 419–440, Progr. Math. 220, Birkhauser Boston, Boston, MA, 2004.Google Scholar
  9. 9.
    Watson G.N.: A treatise on the theory of Bessel functions. Cambridge University Press, Cambridge (1944)MATHGoogle Scholar
  10. 10.
    M. Young, The second moment of GL(3) × GL(2)L-functions at special points, arXiv:0903.1579v1.Google Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia

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