TY - JOUR
T1 - On polynomially normal lattice configurations
AU - Levin, Mordechay B.
AU - Smorodinsky, Meir
PY - 2006/1
Y1 - 2006/1
N2 - In this paper we extend Champernowne's construction of a normal sequence in base b to the ℕ2 case and obtain an explicit construction of the generic point of the ℕ2 shift transformation of the set {0,1,...,b-1}ℕ2. We prove that the intersection of the constructed configuration with an arbitrary polynomial curve in the plane is a normal sequence in base b.
AB - In this paper we extend Champernowne's construction of a normal sequence in base b to the ℕ2 case and obtain an explicit construction of the generic point of the ℕ2 shift transformation of the set {0,1,...,b-1}ℕ2. We prove that the intersection of the constructed configuration with an arbitrary polynomial curve in the plane is a normal sequence in base b.
KW - Normal numbers
KW - Uniform distribution
UR - http://www.scopus.com/inward/record.url?scp=31144478566&partnerID=8YFLogxK
U2 - 10.1007/s00605-005-0340-1
DO - 10.1007/s00605-005-0340-1
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AN - SCOPUS:31144478566
SN - 0026-9255
VL - 147
SP - 137
EP - 153
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
IS - 2
ER -