TY - JOUR
T1 - On Weyl products and uniform distribution modulo one
AU - Aistleitner, Christoph
AU - Larcher, Gerhard
AU - Pillichshammer, Friedrich
AU - Eddin, Sumaia Saad
AU - Tichy, Robert F.
PY - 2018
Y1 - 2018
N2 - In the present paper we study the asymptotic behavior of trigonometric products of the form (Formula presented.) for (Formula presented.), where the numbers (Formula presented.) are evenly distributed in the unit interval [0, 1]. The main result are matching lower and upper bounds for such products in terms of the star-discrepancy of the underlying points (Formula presented.), thereby improving earlier results obtained by Hlawka (Number theory and analysis (Papers in Honor of Edmund Landau, Plenum, New York), 97–118, 1969). Furthermore, we consider the special cases when the points (Formula presented.) are the initial segment of a Kronecker or van der Corput sequences The paper concludes with some probabilistic analogues.
AB - In the present paper we study the asymptotic behavior of trigonometric products of the form (Formula presented.) for (Formula presented.), where the numbers (Formula presented.) are evenly distributed in the unit interval [0, 1]. The main result are matching lower and upper bounds for such products in terms of the star-discrepancy of the underlying points (Formula presented.), thereby improving earlier results obtained by Hlawka (Number theory and analysis (Papers in Honor of Edmund Landau, Plenum, New York), 97–118, 1969). Furthermore, we consider the special cases when the points (Formula presented.) are the initial segment of a Kronecker or van der Corput sequences The paper concludes with some probabilistic analogues.
KW - Kronecker sequence
KW - Star-discrepancy
KW - Trigonometric product
KW - van der Corput sequence
UR - http://www.scopus.com/inward/record.url?scp=85029901955&partnerID=8YFLogxK
U2 - 10.1007/s00605-017-1100-8
DO - 10.1007/s00605-017-1100-8
M3 - Article
AN - SCOPUS:85029901955
SN - 0026-9255
VL - 185
SP - 365
EP - 391
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
IS - 3
ER -