On the Lower Bound in the Lattice Point Remainder Problem for a Parallelepiped

Mordechay B. Levin

doi:10.1007/s00454-015-9728-4

On the Lower Bound in the Lattice Point Remainder Problem for a Parallelepiped

Mordechay B. Levin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let Γ ⊂ R^s be a lattice, obtained from a module in a totally real algebraic number field. Let G be an axis parallel parallelepiped, and let |G| be a volume of G. In this paper we prove that (Formula Presented.). Thus the known estimate (Formula Presented.) is exact. We obtain also a similar result for the low discrepancy sequence corresponding to Γ.

Original language	English
Pages (from-to)	826-870
Number of pages	45
Journal	Discrete and Computational Geometry
Volume	54
Issue number	4
DOIs	https://doi.org/10.1007/s00454-015-9728-4
State	Published - 1 Sep 2015

Bibliographical note

Publisher Copyright:
© 2015, Springer Science+Business Media New York.

Keywords

Lattice point problem
Low discrepancy sequences
Totally real algebraic number field

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10.1007/s00454-015-9728-4

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KW - Totally real algebraic number field

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On the Lower Bound in the Lattice Point Remainder Problem for a Parallelepiped

Abstract

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