Lattice points in elliptic paraboloids
Chamizo Lorente, Fernando (Universidad Autónoma de Madrid. Departamento de Matemáticas)
Pastor, Carlos (Instituto de Ciencias Matemáticas (Madrid, Espanya))

Date:	2019
Abstract:	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.
Grants:	Ministerio de Economía y Competitividad MTM2014-56350-P
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Elliptic paraboloids ; Lattice point problem ; Exponential sums
Published in:	Publicacions matemàtiques, Vol. 63 Núm. 1 (2019) , p. 343-360 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/347179
DOI: 10.5565/PUBLMAT6311912

18 p, 391.6 KB

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