Abstract
The main purpose of this paper is to use estimates for character sums and analytic methods to study the first power mean of the inversion of Dirichlet L–functions with the weight of general quadratic Gauss sums, and three asymptotic formulae are obtained.
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References
Cochrane, T., Zheng, Z. Y.: Pure and mixed exponential sums. Acta Arithmetica, 91, 249–278 (1999)
Apostol, T. M.: Introduction to Analytic Number Theory, New York: Springer-Verlag (1976)
Hua, L. K.: Introduction to Number Theory, Beijing: Science Press (1979)
Burgess, D. A.: On character sums and L-series. Proc. London Math. Soc., 12, 193–206 (1962)
Zhang W. P.: On the average of inversion of Dirichlet L-functions. Compositio Mathematica, 84, 53–57(1992)
Chowla, S.: On Kloostermann’s sum. Norkse Vid. Selbsk. Fak. Frondheim, 40, 70–72 (1967)
Malyshev, A. V.: A generalization of Kloostermann sums and their estimates (in Russian). Vestnik Leningrad Univ., 15, 59–75 (1960)
Estermann, T.: On Kloostermann’s sum. Mathematica, 8, 83–86 (1961)
Vaughan, R. C.: An elementary method in prime number theory. Recent Progress in Analytic Number Theory, Academic Press, 1, 341–347 (1998)
Davenport, H.: Multiplicative number theory, Markham (1967)
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This work is supported by the NSF and the PNSF of P. R. China
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Zhang, W.P. The First Power Mean of the Inversion of L–Functions Weighted by Quadratic Gauss Sums. Acta Math Sinica 20, 283–292 (2004). https://doi.org/10.1007/s10114-003-0243-9
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DOI: https://doi.org/10.1007/s10114-003-0243-9