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A further generalization of Hilbert's inequality

Part of: Inequalities

Published online by Cambridge University Press:  26 February 2010

Hugh L. Montgomery  and
Jeffrey D. Vaaler
Hugh L. Montgomery
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, U.S.A.
Jeffrey D. Vaaler
Affiliation:
Department of Mathematics, The University of Texas, Austin, TX 78712, U.S.A.
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Extract

Hilbert's inequality asserts that

for arbitrary complex numbers ar. The constant π was first obtained by Schur [5], and is best possible. Following a suggestion of Selberg, Montgomery and Vaughan [4] showed that

where the γr are distinct real numbers and

MSC classification

Secondary: 26D20: Other analytical inequalities
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 35 - 39
Copyright
Copyright © University College London 1999

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References

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4.Montgomery, H. L. and Vaughan, R. C.. Hilbert's Inequality. J. London Math. Soc. (2) 8 (1974), 73–82.CrossRefGoogle Scholar
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