TY - JOUR

T1 - Pair correlation of fractional parts derived from rational valued sequences, II

AU - Chaubey, Sneha

AU - Lanius, Melinda

AU - Zaharescu, Alexandru

N1 - Publisher Copyright:
© 2015 Elsevier Inc.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - A rational valued vector sequence x→, for some fixed k and r∈N, is a map x→:Nk→Qr. In the present paper, we complement the results of [3] with a discussion on rational valued vector sequences. We investigate the pair correlation function for the fractional parts of sequences t→{dot operator}x→, where x→ is a rational valued vector sequence and t→∈Rr. We offer a new class of sequences x→ whose pair correlation function behaves as that of random sequences for almost all real vectors t→, namely, injective sequences of the formx→(m,n)=(p1mp2nb→(m,n),p3mp4nb→(m,n)) for p1, p2, p3, and p4 primes and where b→:N2→N satisfies a certain growth condition.

AB - A rational valued vector sequence x→, for some fixed k and r∈N, is a map x→:Nk→Qr. In the present paper, we complement the results of [3] with a discussion on rational valued vector sequences. We investigate the pair correlation function for the fractional parts of sequences t→{dot operator}x→, where x→ is a rational valued vector sequence and t→∈Rr. We offer a new class of sequences x→ whose pair correlation function behaves as that of random sequences for almost all real vectors t→, namely, injective sequences of the formx→(m,n)=(p1mp2nb→(m,n),p3mp4nb→(m,n)) for p1, p2, p3, and p4 primes and where b→:N2→N satisfies a certain growth condition.

KW - Fractional parts

KW - Pair correlation

KW - Rational valued sequences

KW - Vector sequences

UR - http://www.scopus.com/inward/record.url?scp=84939447601&partnerID=8YFLogxK

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U2 - 10.1016/j.jnt.2015.06.021

DO - 10.1016/j.jnt.2015.06.021

M3 - Article

AN - SCOPUS:84939447601

VL - 158

SP - 151

EP - 164

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -