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Lattice points in the 3-dimensional torus

Author
Chamizo Lorente, Fernandountranslated; Raboso, Dulcinea
Entity
UAM. Departamento de Matemáticas
Publisher
Elsevier
Date
2015-01-01
Citation
Journal of Mathematical Analysis and Applications 429.2 (2015): 733-743
ISSN
0022-247X (print)
DOI
10.1016/j.jmaa.2015.04.053
Editor's Version
http://dx.doi.org/10.1016/j.jmaa.2015.04.053
Subjects
Exponential sums; Lattice point problems; Poisson summation formula; Matemáticas
URI
http://hdl.handle.net/10486/669373
Rights
© 2015 Elsevier Inc.

Abstract

We prove the exponent 4/3 for the lattice point discrepancy of a torus in R3 (generated by the rotation of a circle around the z axis). The exponent comes from a diagonal term and it seems a natural limit for any approach based solely on classical methods of exponential sums. The result extends to other solids in R3 related to the torus
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Google™ Scholar:Chamizo Lorente, Fernando - Raboso, Dulcinea

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