Weyl Sums over Integers with Digital Restrictions
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in: Michigan mathematical journal, Jahrgang 2023, Nr. ??? Stand: 25. Juli 2023, 22.01.2023.
Publikationen: Beitrag in Fachzeitschrift › Artikel › Forschung › (peer-reviewed)
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TY - JOUR
T1 - Weyl Sums over Integers with Digital Restrictions
AU - Shparlinski, Igor
AU - Thuswaldner, Jörg
PY - 2023/1/22
Y1 - 2023/1/22
N2 - 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 established by Bourgain, Demeter, and Guth (2016) and Wooley (2016, 2019). We use our result to give an estimate of the discrepancy of point sets defined by the values of polynomials at arguments having the sum of binary digits restricted in different ways.
AB - 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 established by Bourgain, Demeter, and Guth (2016) and Wooley (2016, 2019). We use our result to give an estimate of the discrepancy of point sets defined by the values of polynomials at arguments having the sum of binary digits restricted in different ways.
U2 - 10.1307/mmj/20216094
DO - 10.1307/mmj/20216094
M3 - Article
VL - 2023
JO - Michigan mathematical journal
JF - Michigan mathematical journal
SN - 0026-2285
IS - ??? Stand: 25. Juli 2023
ER -