TY - JOUR
T1 - Pair correlation of fractional parts derived from rational valued sequences
AU - Chaubey, Sneha
AU - Lanius, Melinda
AU - Zaharescu, Alexandru
N1 - Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2015/6/1
Y1 - 2015/6/1
N2 - We investigate the pair correlation of the sequence of fractional parts of αxn, n∈N, where xn is rational valued and α is a real number. As examples, we offer two classes of sequences xn whose pair correlation behaves as that of random sequences for almost all real numbers α. First, sequences of the form xn=an/bn where an is lacunary and bn satisfies a certain growth condition. Second, sequences of the form xn=gn/2ω(n) for a positive integer g which is not a power of 2 and where ω(n) denotes the number of distinct prime factors of n.
AB - We investigate the pair correlation of the sequence of fractional parts of αxn, n∈N, where xn is rational valued and α is a real number. As examples, we offer two classes of sequences xn whose pair correlation behaves as that of random sequences for almost all real numbers α. First, sequences of the form xn=an/bn where an is lacunary and bn satisfies a certain growth condition. Second, sequences of the form xn=gn/2ω(n) for a positive integer g which is not a power of 2 and where ω(n) denotes the number of distinct prime factors of n.
KW - Fractional parts of sequences
KW - Pair correlation
KW - Rational valued sequences
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U2 - 10.1016/j.jnt.2014.12.014
DO - 10.1016/j.jnt.2014.12.014
M3 - Article
AN - SCOPUS:84922539497
VL - 151
SP - 147
EP - 158
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
ER -