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On the distribution of lattice points on spheres and level surfaces of polynomials

✍ Scribed by Akos Magyar

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
168 KB
Volume
122
Category
Article
ISSN
0022-314X

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✦ Synopsis

The irregularities of distribution of lattice points on spheres and on level surfaces of polynomials are measured in terms of the discrepancy with respect to caps. It is found that the discrepancy depends on diophantine properties of the direction of the cap. If the direction of the cap is diophantine, in case of the spheres, close to optimal upper bounds are found. The estimates are based on a precise description of the Fourier transform of the set of lattice points on polynomial surfaces.

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