Local mean value estimates for Weyl sums

Julia Brandes; Changhao Chen; Igor Shparlinski

doi:10.4171/rmi/1495

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
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Changhao Chen
Anhui University, Hefei, P. R. China
- MathSciNet
- zbMATH Open
Igor Shparlinski
University of New South Wales, Sydney, Australia
- MathSciNet
- ORCID

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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