JournalsrmiVol. 40, No. 6pp. 2095–2134

Local mean value estimates for Weyl sums

  • Julia Brandes

    University of Gothenburg and Chalmers Institute of Technology, Göteborg, Sweden

  • Changhao Chen

    Anhui University, Hefei, P. R. China

  • Igor Shparlinski

    University of New South Wales, Sydney, Australia
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Abstract

We obtain new estimates –both upper and lower bounds– on the mean values of the Weyl sums over a small box inside of the unit torus. In particular, we refine recent conjectures of C. Demeter and B. Langowski (2022), and improve some of their results.

Cite this article

Julia Brandes, Changhao Chen, Igor Shparlinski, Local mean value estimates for Weyl sums. Rev. Mat. Iberoam. 40 (2024), no. 6, pp. 2095–2134

DOI 10.4171/RMI/1495