[Zurück]


Buchbeiträge:

M. Drmota, R. Hofer, G. Larcher:
"On the Discrepancy of Halton-Kronecker Sequences";
in: "Number Theory - Diophantine Problems, Uniform Distribution and Applications", herausgegeben von: Springer, Cham; Springer International Publishing, 2017, ISBN: 978-3-319-55356-6, S. 219 - 226.



Kurzfassung englisch:
We study the discrepancy DN of sequences (z n ) n≥1 =((x n ,y n )) n≥0 ∈[0,1) s+1
(zn)n≥1=((xn,yn))n≥0∈[0,1)s+1
where (x n ) n≥0
(xn)n≥0
is the s-dimensional Halton sequence and (y n ) n≥1
(yn)n≥1
is the one-dimensional Kronecker-sequence ({nα}) n≥1
({nα})n≥1
. We show that for α algebraic we have ND N =O(N ε )
NDN=O(Nε)
for all ɛ > 0. On the other hand, we show that for α with bounded continued fraction coefficients we have ND N =O(N 12 (logN) s )
NDN=O(N12(log⁡N)s)
which is (almost) optimal since there exist α with bounded continued fraction coefficients such that ND N =Ω(N 12 )
NDN=Ω(N12).
Dedicated to Robert F. Tichy on the occasion of his 60th birthday


"Offizielle" elektronische Version der Publikation (entsprechend ihrem Digital Object Identifier - DOI)
http://dx.doi.org/10.1007/978-3-319-55357-3_10


Erstellt aus der Publikationsdatenbank der Technischen Universitšt Wien.