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A NOTE ON THE SECOND MOMENT OF AUTOMORPHIC L-FUNCTIONS

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  10 December 2009

H. M. Bui
H. M. Bui*
Affiliation:
Mathematical Institute, University of Oxford, Oxford, OX1 3LB, U.K. (email: [email protected])
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Abstract

We obtain the formula for the twisted harmonic second moment of the L-functions associated with primitive Hecke eigenforms of weight 2. A consequence of our mean-value theorem is reminiscent of recent results of Conrey and Young on the reciprocity formula for the twisted second moment of Dirichlet L-functions.

MSC classification

Secondary: 11M06: $zeta (s)$ and $L(s, chi)$
Type
Research Article
Information
Mathematika , Volume 56 , Issue 1 , January 2010 , pp. 35 - 44
Copyright
Copyright © University College London 2010

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References

[1]Conrey, J. B., The mean-square of Dirichlet L-functions, http://arxiv.org/abs/0708.2699.Google Scholar
[2]Deligne, P., Le conjecture de Weil I. Publ. Math. Inst. Hautes. Études. Sci. 43 (1974), 273–307.CrossRefGoogle Scholar
[3]Iwaniec, H. and Sarnak, P., The non-vanishing of central values of automorphic L-functions and Landau–Siegel zeros. Israel J. Math. 120 (2000), 155–177.CrossRefGoogle Scholar
[4]Jutila, M., Lectures on a Method in the Theory of Exponential Sums (Tata Lectures on Mathematics and Physics, 80), Springer (Berlin, 1987).Google Scholar
[5]Kowalski, E. and Michel, P., A lower bound for the rank of J 0(q). Acta Arith. 94(4) (2000), 303–343.CrossRefGoogle Scholar
[6]Kowalski, E., Michel, P. and VanderKam, J. M., Mollification of the fourth moment of automorphic L-functions and arithmetic applications. Invent. Math. 142 (2000), 95–151.CrossRefGoogle Scholar
[7]Young, M. P., The reciprocity law for the twisted second moment of Dirichlet L-functions, http://arxiv.org/abs/0708.2928.Google Scholar