Abstract

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→⋅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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.