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On the mean-square of the error term related to Σn⩽xλ2(n j)

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Abstract

We prove a non-trivial upper bound for the quantity

$\int_X^{2X} {\left| {\sum\limits_{n \leqslant x} {\lambda ^2 \left( {n^j } \right) - c_{\left( {j - 1} \right)} x} } \right|^2 dx}$

for j = 2, 3, 4.

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Authors and Affiliations

  1. Department of Mathematics, Shandong Normal University, Jinan, 250014, China

    HuiXue Lao

  2. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India

    Ayyadurai Sankaranarayanan

Authors
  1. HuiXue Lao
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  2. Ayyadurai Sankaranarayanan
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Correspondence to Ayyadurai Sankaranarayanan.

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Lao, H., Sankaranarayanan, A. On the mean-square of the error term related to Σn⩽xλ2(n j). Sci. China Math. 54, 855–864 (2011). https://doi.org/10.1007/s11425-011-4175-z

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  • DOI: https://doi.org/10.1007/s11425-011-4175-z

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