2021/05/11 by Igor E. Shparlinski, Shparlinski, Igor E., Jörg Μ. Thuswaldner +1 · 1 citation
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2105.04835
openalex publication_date 2021/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We estimate Weyl sums over the integers with sum of binary digits either fixed or restricted by some congruence condition. In our proofs we use ideas that go back to a paper by Banks, Conflitti and the first author (2002). Moreover, we apply the "main conjecture" on the Vinogradov mean value theorem which has been established by Bourgain, Demeter and Guth (2016) as well as by Wooley (2016, 2019). We use our result to give an estimate of the discrepancy of point sets that are defined by the values of polynomials at arguments having the sum of binary digits restricted in different ways.