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A further generalization of Hilbert's inequality
Published online by Cambridge University Press: 26 February 2010
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
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- Copyright © University College London 1999
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