Lattice points in elliptic paraboloids

We consider the lattice point problem corresponding to a family of elliptic paraboloids in Rd with d ≥ 3 and we prove the expected to be optimal exponent, improving previous results. This is especially noticeable for d = 3 because the optimal exponent is conjectural even for the sphere. We also trea...

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Detalles Bibliográficos
Autores: Chamizo Lorente, Fernando|||0000-0003-2793-7920, Pastor, Carlos
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:200755
Acceso en línea:https://ddd.uab.cat/record/200755
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6311912
Access Level:acceso abierto
Palabra clave:Elliptic paraboloids
Lattice point problem
Exponential sums
Descripción
Sumario:We consider the lattice point problem corresponding to a family of elliptic paraboloids in Rd with d ≥ 3 and we prove the expected to be optimal exponent, improving previous results. This is especially noticeable for d = 3 because the optimal exponent is conjectural even for the sphere. We also treat some aspects of the case d = 2, getting for a simple parabolic region an Ω-result that is unknown for the classical circle and divisor problems.