Abstract
In this work an asymptotic formula (with a powerlike residue of degree) is proved for the quadratic mean over the critical line of the Dirichlet series associated with the cusp form of weight zero for modular group. The proof is based on author's different formulas of summation for Kloosterman sums.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 109, pp. 93–130, 1981.
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Kuznetsov, N.V. Mean value of the Hecke series associated with the cusp forms of weight zero. J Math Sci 24, 215–238 (1984). https://doi.org/10.1007/BF01087243
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DOI: https://doi.org/10.1007/BF01087243