A lower bound for the b-adic diaphony
نویسندگان
چکیده
La diafonia b-adica è una misura quantitativa della irregularità di distribuzione di un insieme di punti nel cubo unità s-dimensionale. In questi appunti mostriamo che la diafonia b-adica (per un numero primo b) di un insieme di N punti nel cubo unità di dimensione s è sempre almeno di ordine (logN)(s−1)/2/N . Questo limite inferiore è il migliore possibile. Abstract The b-adic diaphony is a quantitative measure for the irregularity of distribution of a point set in the s-dimensional unit cube. In this note we show that the b-adic diaphony (for prime b) of a point set consisting of N points in the s-dimensional unit cube is always at least of order (logN)(s−1)/2/N . This lower bound is best possible.The b-adic diaphony is a quantitative measure for the irregularity of distribution of a point set in the s-dimensional unit cube. In this note we show that the b-adic diaphony (for prime b) of a point set consisting of N points in the s-dimensional unit cube is always at least of order (logN)(s−1)/2/N . This lower bound is best possible.
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