Abstract
Fouvry and Iwaniec's method ([6], [11]) for exponential sums with monomials uses, in a crucial way, a spacing lemma for t(m, q) := (m + q)α − (m − q)α. By introducing a technique on integer points close to a family of curves, we are able to improve their result and to treat the spacing problem for u(m, n, q) := t(m, q)n β. Finally we choose four classic arithmetic problems to illustrate our new results.
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Sargos, P., Wu, J. Multiple Exponential Sums with Monomials and Their Applications in Number Theory. Acta Mathematica Hungarica 87, 333–354 (2000). https://doi.org/10.1023/A:1006777803163
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DOI: https://doi.org/10.1023/A:1006777803163