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The mean value theorem for the Riemann zeta-function

Published online by Cambridge University Press:  26 February 2010

D. R. Heath-Brown
D. R. Heath-Brown
Affiliation:
Trinity College, Cambridge CB2 1TQ.
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Extract

In this paper we shall consider the well known mean value theorem,

where γ is Euler's constant. The error term E(T) has been estimated by various writers; in particular the bounds E(T) = o(T log T), E(T) ≪ T1/2 log T, E(T) ≪ T5/12(log T)2 and

where ε is any positive quantity, have been given by Hardy and Littlewood [7], Ingham [8], Titchmarsh [10], and Balasubramanian [2], respectively.

Type
Research Article
Information
Mathematika , Volume 25 , Issue 2 , December 1978 , pp. 177 - 184
Copyright
Copyright © University College London 1978

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References

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