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Three-dimensional exponential sums with monomials
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Published/Copyright:
May 8, 2006
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).
Received: 2002-03-12
Published Online: 2006-05-08
Published in Print: 2006-02-24
© Walter de Gruyter
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- Three-dimensional exponential sums with monomials
- A Fourier transformation for Higgs bundles
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Articles in the same Issue
- Three-dimensional exponential sums with monomials
- A Fourier transformation for Higgs bundles
- Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane
- Kähler quantization and reduction
- Traces of Hecke operators acting on three-dimensional hyperbolic space
- Teitelbaum's exceptional zero conjecture in the function field case
- Symmetries, quotients and Kähler-Einstein metrics
- Smoothing of ribbons over curves
