Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
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Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"
Image for the paper "Energy bounds for modular roots and their applications"

Energy bounds for roots

Number theory

Bounds for additive energies of modular roots can be generalised and improved with tools from additive combinatorics and algebraic number theory.

Energy bounds for modular roots and their applications

Journal of the Institute of Mathematics of Jussieu, in press  (2021)

B. Kerr, I. Shkredov, I. Shparlinski, A. Zaharescu

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 Salie sums and to a new equidistribution estimate for the set of modular roots of primes.

Journal of the Institute of Mathematics of Jussieu, in press  (2021)

B. Kerr, I. Shkredov, I. Shparlinski, A. Zaharescu