Borda, Bence (2018) Lattice Points in Algebraic Cross-polytopes and Simplices. DISCRETE AND COMPUTATIONAL GEOMETRY, 60 (1). pp. 145-169. ISSN 0179-5376
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Abstract
The number of lattice points , as a function of the real variable is studied, where belongs to a special class of algebraic cross-polytopes and simplices. It is shown that the number of lattice points can be approximated by an explicitly given polynomial of t depending only on P. The error term is related to a simultaneous Diophantine approximation problem for algebraic numbers, as in Schmidt's theorem. The main ingredients of the proof are a Poisson summation formula for general algebraic polytopes, and a representation of the Fourier transform of the characteristic function of an arbitrary simplex in the form of a complex line integral.
| Item Type: | Article |
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| Additional Information: | FELTÖLTŐ: Szakonyi Erzsebet szakonyi.erzsebet@renyi.mta.hu |
| Uncontrolled Keywords: | APPROXIMATION; Polynomials; Polytope; Computer Science, Theory & Methods; Lattice point; Poisson summation; GEOMETRIE DIOPHANTIENNE LINEAIRE; SUR UN PROBLEME; INTEGER POINTS; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 12 Jan 2019 04:52 |
| Last Modified: | 12 Jan 2019 04:52 |
| URI: | http://real.mtak.hu/id/eprint/89745 |
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