TY - JOUR
T1 - Weyl Sums over Integers with Digital Restrictions
AU - Shparlinski, Igor E.
AU - Thuswaldner, Jörg
N1 - Publisher Copyright: © 2024 University of Michigan. All rights reserved.
PY - 2024/2/25
Y1 - 2024/2/25
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.
UR - http://www.scopus.com/inward/record.url?scp=85186559672&partnerID=8YFLogxK
M3 - Article
SN - 0026-2285
VL - 74.2023
SP - 189
EP - 214
JO - Michigan mathematical journal
JF - Michigan mathematical journal
IS - 1
ER -