Ultra-short sums of trace functions

Published 27 Feb 2023 in math.NT | (2302.13670v2)

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.

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