A Discrete Fourier Kernel and Fraenkel's Tiling Conjecture

Details A Discrete Fourier Kernel and Fraenkel's Tiling Conjecture A Discrete Fourier Kernel and Fraenkel's Tiling Conjecture

2004-07-17

arxiv.org/abs/math/0407306v2

Acta Arith. 118 (2005), no. 3, 283--304.

Mathematics

Number Theory

24 pages, 6 figures (now with minor revisions and clarifications)

Scientific paper

The set B_{p,r}^q:=\{\floor{nq/p+r} \colon n\in Z \} with integers p, q, r) is a Beatty set with density p/q. We derive a formula for the Fourier transform \hat{B_{p,r}^q}(j):=\sum_{n=1}^p e^{-2 \pi i j \floor{nq/p+r} / q}. A. S. Fraenkel conjectured that there is essentially one way to partition the integers into m>2 Beatty sets with distinct densities. We conjecture a generalization of this, and use Fourier methods to prove several special cases of our generalized conjecture.

Affiliated with

Also associated with

No associations

Rating

A Discrete Fourier Kernel and Fraenkel's Tiling Conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Discrete Fourier Kernel and Fraenkel's Tiling Conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Discrete Fourier Kernel and Fraenkel's Tiling Conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-12115