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References (11)
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Multiple Exponential Sums with Monomials and Their Applications in Number TheoryActa Mathematica Hungarica, 87
- Publisher
- de Gruyter
- Copyright
- © Walter de Gruyter
- ISSN
- 0075-4102
- eISSN
- 1435-5345
- DOI
- 10.1515/CRELLE.2006.012
- Publisher site
- See Article on Publisher Site
Abstract
Fouvry and Iwaniec's theorem concerning three-dimensional exponential sums with monomials relies on a spacing lemma whose optimal form is yet unproved. We bypass their spacing lemma via a diophantine problem in four variables and we obtain the expected bound in their theorem. In the problem of abelian groups of a given order, this yields the exponent 1/4 + ϵ, a result close to a conjecture of H. E. Richert (1952).
Journal
Journal für die reine und angewandte Mathematik (Crelle's Journal) – de Gruyter
Published: Feb 24, 2006