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On the mean square of dirichletL-functions

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Abstract

In the present paper we establish a sharp asymptotic formula for\(\sum\limits_{x\bmod q} {\smallint _0^T } |L(\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} + it,x)|^2 dt\) with an error term\(O(T^{\frac{1}{3} - \delta + e} )\) (σ is a suitable positive constant) uniformly inq andT, which improves the best result hitherto given.

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  1. Institute of Mathematics, Shandong University, PRC

    Zhan Tao

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  1. Zhan Tao
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Project supported by the National Natural Science Foundation of China

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Tao, Z. On the mean square of dirichletL-functions. Acta Mathematica Sinica 8, 204–224 (1992). https://doi.org/10.1007/BF02629940

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  • DOI: https://doi.org/10.1007/BF02629940

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