Lattice points in bodies of revolution

Chamizo, Fernando

doi:10.4064/aa-85-3-265-277

Cited by 25 publications

(33 citation statements)

References 7 publications

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“…A standard analytic tool to avoid this problem is to introduce some smoothing in χ. We proceed as in Proposition 2.1 of [Cha98]. For the sake of completeness we include here a proof.…”

Section: The Application Of the Poisson Summation Formulamentioning

confidence: 99%

Lattice points in the 3-dimensional torus

Chamizo

Raboso

2015

Journal of Mathematical Analysis and Applications

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Esta es la versión de autor del artículo publicado en: This is an author produced version of a paper published in: El acceso a la versión del editor puede requerir la suscripción del recurso Access to the published version may require subscription LATTICE POINTS IN THE 3-DIMENSIONAL TORUSFERNANDO CHAMIZO AND DULCINEA RABOSO Abstract. We prove the exponent 4/3 for the lattice point discrepancy of a torus in R 3 (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 R 3 related to the torus.

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“…A standard analytic tool to avoid this problem is to introduce some smoothing in χ. We proceed as in Proposition 2.1 of [Cha98]. For the sake of completeness we include here a proof.…”

Section: The Application Of the Poisson Summation Formulamentioning

confidence: 99%

Lattice points in the 3-dimensional torus

Chamizo

Raboso

2015

Journal of Mathematical Analysis and Applications

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“…We shall denote them by R in the sequel. For the case of nonzero curvature of the boundary, F. Chamizo [2] obtained the upper bound…”

Section: Bodies Of Rotationmentioning

confidence: 99%

On the lattice discrepancy of bodies of rotation with boundary points of curvature zero

Nowak

2008

Arch. Math.

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“…In this case, 4) according to F. Chamizo [1], and 5) as was shown by the first named author [12], on the basis of a deep and fairly general method of J.L. Hafner [3].…”

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confidence: 91%

“…Introduction. We consider a compact convex body B in R 3 which contains the origin as an inner point and assume that its boundary ∂B is a C ∞ surface (1) with bounded nonzero Gaussian curvature throughout. For a large real parameter t , we consider a linearly dilated copy √ t B of B , and in particular its lattice point discrepancy…”

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confidence: 99%

The lattice point discrepancy of a body of revolution: Improving the lower bound by Soundararajan?s method

Kühleitner

Nowak

2004

Arch. Math.

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Abstract.For a convex body B in R 3 which is invariant under rotations around one coordinate axis and has a smooth boundary of bounded nonzero curvature, the lattice point discrepancy P B (t) (number of integer points minus volume) of a linearly dilated copy √ tB is estimated from below. On the basis of a recent method of K. Soundararajan [16] an Ω -bound is obtained that improves upon all earlier results of this kind.

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Lattice points in bodies of revolution

Cited by 25 publications

References 7 publications

Lattice points in the 3-dimensional torus

Lattice points in the 3-dimensional torus

On the lattice discrepancy of bodies of rotation with boundary points of curvature zero

The lattice point discrepancy of a body of revolution: Improving the lower bound by Soundararajan?s method

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