Ultra-short sums of trace functions
Volume 210 / 2023
Acta Arithmetica 210 (2023), 367-390
MSC: Primary 11T23; Secondary 11L15.
DOI: 10.4064/aa230308-11-5
Published online: 29 June 2023
Abstract
We generalize results of Duke, Garcia, Hyde, Lutz and others on the distribution of sums of roots of unity related to Gaussian periods to obtain equidistribution of similar sums over zeros of arbitrary integral polynomials. We also interpret these results in terms of trace functions, and generalize them to higher rank trace functions.
