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On cubic residues and related problems

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Abstract

In this paper, we use elementary methods to transform sums involving cubic residues into expressions involving Gauss sums. Following this, we use properties of third-order characters and the product formula for the classical Gauss sums to study problems on the computation of cubic residues on some special integer sets. We give some exact formulae for the corresponding counting functions.

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Acknowledgements

The authors would like to thank the editor and referees for their helpful suggestions and comments that significantly improve the presentation of this work.

Funding

This work is supported by the N. S. F. (12126357) of P. R. China.

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Author notes

  1. Wenpeng Zhang contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics, Northwest University, Xuefu Street No. 1, Xi’an, 710100, Shaanxi, China

    Xiaodan Yuan & Wenpeng Zhang

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  1. Xiaodan Yuan
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  2. Wenpeng Zhang
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Correspondence to Xiaodan Yuan.

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The authors declare that there are no conflicts of interest regarding the publication of this work.

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All authors have contributed equally to this work. All authors read and approved the final manuscript.

Additional information

Communicated by B. Sury.

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Yuan, X., Zhang, W. On cubic residues and related problems. Indian J Pure Appl Math 54, 806–815 (2023). https://doi.org/10.1007/s13226-022-00299-6

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  • DOI: https://doi.org/10.1007/s13226-022-00299-6

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