Local mean value estimates for Weyl sums

• Julia Brandes ^[1] ; Changhao Chen ^[2] ; Igor Shparlinski ^[3]
  1. [1] University of Gothenburg

     University of Gothenburg

     Suecia

     
  2. [2] Anhui University

     Anhui University

     China

     
  3. [3] University of New South Wales, Sydney, Australia

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 6, 2024, págs. 2095-2134
• Idioma: inglés
• DOI: 10.4171/RMI/1495
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• Resumen

  • 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.