A Note on Nyman–Beurling’s Approach to the Riemann Hypothesis

The Nyman–Beurling’s theorem states that the Riemann hypothesis is true if and only if the set of all linear combination of the functions u α ( x ) : = [ α / x ] - α [ 1 / x ] is dense in L 2 ( 0 , 1 ) . In this note we show that if a function has a nonzero limit at the origin, the function is not o...

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Bibliographic Details
Published in:Integral equations and operator theory 2015-11, Vol.83 (3), p.447-449
Main Author: Yang, Jongho
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:The Nyman–Beurling’s theorem states that the Riemann hypothesis is true if and only if the set of all linear combination of the functions u α ( x ) : = [ α / x ] - α [ 1 / x ] is dense in L 2 ( 0 , 1 ) . In this note we show that if a function has a nonzero limit at the origin, the function is not orthogonal to some u α .
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-015-2259-9