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arXiv · 2103.09405

Energy bounds for modular roots and their applications

Bryce Kerr·Ilya D. Shkredov·Igor E. Shparlinski·Alexandru Zaharescu
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Abstract

We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between {\it Sali{\'e}} sums and to a new equidistribution estimate for the set of modular roots of primes.

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Bryce Kerr, Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu. 2021-03-17. Energy bounds for modular roots and their applications. https://doi.org/10.1017/s1474748023000397

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