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...

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Detalles Bibliográficos
Autores: Chamizo Lorente, Fernando, Raboso, Dulcinea
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/669373
Acceso en línea:http://hdl.handle.net/10486/669373
https://dx.doi.org/10.1016/j.jmaa.2015.04.053
Access Level:acceso abierto
Palabra clave:Exponential sums
Lattice point problems
Poisson summation formula
Matemáticas
Descripción
Sumario: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