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On integer solutions of Parsell–Vinogradov systems

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We prove a sharp upper bound on the number of integer solutions of the Parsell–Vinogradov system in every dimension \(d\ge 2\).

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Acknowledgements

The authors thank Ciprian Demeter for numerous discussions on related topics. The first author thanks Julia Brandes and Lillian Pierce for discussions on applications of their result. Part of this work is contained in the PhD thesis [43] of the second author. He would like to thank his advisor Peter Sarnak for a lot of very helpful discussions. Part of this material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the first author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring semester of 2017. The work of the second author is supported by the National Science Foundation under Grant No. 1638352 and the James D. Wolfensohn Fund.

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  1. Shaoming Guo & Ruixiang Zhang

    Present address: Department of Mathematics, University of Wisconsin Madison, Madison, WI, 53706, USA

Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Ruixiang Zhang

  2. Department of Mathematics, Indiana University, Bloomington, IN, 47405, USA

    Shaoming Guo

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  1. Shaoming Guo
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  2. Ruixiang Zhang
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Correspondence to Ruixiang Zhang.

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Guo, S., Zhang, R. On integer solutions of Parsell–Vinogradov systems. Invent. math. 218, 1–81 (2019). https://doi.org/10.1007/s00222-019-00881-6

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  • DOI: https://doi.org/10.1007/s00222-019-00881-6

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