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math.NT2021★ 4 cited
Energy bounds for modular roots and their applications
Bryce Kerr, Ilya D. Shkredov, Igor E. Shparlinski +1
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, algebra…
math.NT2021
On the cubic Weyl sum
Bryce Kerr
We obtain an estimate for the cubic Weyl sum which improves the bound obtained from Weyl differencing for short ranges of summation. In particular, we show that for any $\varepsilo…