The sixth moment of the family of Γ1(q)-automorphic L-functions
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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
KeywordsAutomorphic forms L-functions Moments
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- 1.J. B. Conrey, H. Iwaniec, and K. Soundararajan, The sixth power moment of Dirichlet L-functions, arXiv: 0710.5176v1Google Scholar
- 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.H. Iwaniec, Automorphic Number Theory, Current Developments in Mathematics, 2003, 35–52.Google Scholar
- 5.H. Iwaniec, Topics in Classical Automorphic Forms, Graduate Studies in Mathematics, 17, American Mathematical Society, Providence, RI, 1997.Google Scholar
- 6.H. Iwaniec and E. Kowalski, Analytic Number Theory, American Mathematical Society Colloquium Publications 53, AMS, Providence, 2004.Google Scholar
- 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
- 10.M. Young, The second moment of GL(3) × GL(2)L-functions at special points, arXiv:0903.1579v1.Google Scholar