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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Gram lines and the average of the real part of the Riemann zeta function
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by Kevin A. Broughan and A. Ross Barnett PDF
Math. Comp. 81 (2012), 1669-1679 Request permission


The contours $\Im \Lambda (s)=0$ of the function which satisfies $\zeta (1-s)=\Lambda (s)\zeta (s)$ cross the critical strip on lines which are almost horizontal and straight, and which cut the critical line alternately at Gram points and points where $\zeta (s)$ is imaginary. When suitably averaged the real part of $\zeta (s)$ satisfies a relation which greatly extends a theorem of Titchmarsh, (namely that the average of $\zeta (s)$ over the Gram points has the value 2), to the open right-hand half plane $\sigma >0$.
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Additional Information
  • Kevin A. Broughan
  • Affiliation: University of Waikato, Hamilton, New Zealand
  • Email:
  • A. Ross Barnett
  • Affiliation: University of Waikato, Hamilton, New Zealand
  • Email:
  • Received by editor(s): November 28, 2010
  • Received by editor(s) in revised form: March 25, 2011, and April 15, 2011
  • Published electronically: December 7, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 1669-1679
  • MSC (2010): Primary 11M06
  • DOI:
  • MathSciNet review: 2904597