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- W2516913948 abstract "The number of lattice points $left| tP cap mathbb{Z}^d right|$, as a function of the real variable $t>1$ is studied, where $P subset mathbb{R}^d$ 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." @default.
- W2516913948 created "2016-09-16" @default.
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- W2516913948 date "2016-08-08" @default.
- W2516913948 modified "2023-09-27" @default.
- W2516913948 title "Lattice points in algebraic cross-polytopes and simplices" @default.
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