A generalization of Beurling's criterion for the Riemann hypothesis

It is known that the Riemann hypothesis holds if and only if the function χ(0,1) can be approximated by linear combinations of uα in L2(0,1). Here uα(x) is defined by [α/x]−α[1/x] for 0

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Bibliographic Details
Published in:Journal of number theory 2016-07, Vol.164, p.299-302
Main Author: Yang, Jongho
Format: Article
Language:English
Subjects:
Bercovici–Foias theorem
Nyman–Beurling theorem
Riemann hypothesis
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Summary:It is known that the Riemann hypothesis holds if and only if the function χ(0,1) can be approximated by linear combinations of uα in L2(0,1). Here uα(x) is defined by [α/x]−α[1/x] for 0
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2016.01.024