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On integer solutions of Parsell–Vinogradov systems

  • Shaoming Guo
  • Ruixiang ZhangEmail author
Article
  • 259 Downloads

Abstract

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

Mathematics Subject Classification

Primary 11L07 Secondary 42A45 

Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA
  3. 3.Department of MathematicsUniversity of Wisconsin MadisonMadisonUSA

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