Lattice points in the 3-dimensional torus
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 o...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Universidad Autónoma de Madrid |
| Repository: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Language: | English |
| OAI Identifier: | oai:repositorio.uam.es:10486/669373 |
| Online Access: | http://hdl.handle.net/10486/669373 https://dx.doi.org/10.1016/j.jmaa.2015.04.053 |
| Access Level: | Open access |
| Keyword: | Exponential sums Lattice point problems Poisson summation formula Matemáticas |
| Summary: | 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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