Weyl sums with multiplicative coefficients and joint equidistribution

Bordignon, Matteo; Bortolotto, Cynthia; Kerr, Bryce

doi:10.2140/ant.2025.19.1549

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Weyl sums with multiplicative coefficients and joint equidistribution

Matteo Bordignon, Cynthia Bortolotto and Bryce Kerr

Vol. 19 (2025), No. 8, 1549–1580

DOI: 10.2140/ant.2025.19.1549

Abstract

We generalise a result of Montgomery and Vaughan regarding exponential sums with multiplicative coefficients to the setting of Weyl sums. As applications, we establish a joint equidistribution result for roots of polynomial congruences and polynomial values which generalises a result of Hooley. We also obtain some new results for mixed character sums.

Keywords

Weyl sums, multiplicative functions

Mathematical Subject Classification

Primary: 11N60, 11N75

Milestones

Received: 18 June 2023

Revised: 21 July 2024

Accepted: 3 September 2024

Published: 12 June 2025

Authors

Matteo Bordignon
Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden	Faculty of Mathematics and Physics Charles University Praha Czech Republic

Cynthia Bortolotto
Department of Mathematics ETH Zürich Zürich Switzerland

Bryce Kerr
University of New South Wales School of Science Canberra Australia

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Vol. 19, No. 8, 2025