## 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

## Abstract:

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 $\sigma >0$.## References

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## Additional Information

**Kevin A. Broughan**- Affiliation: University of Waikato, Hamilton, New Zealand
- Email: kab@waikato.ac.nz
**A. Ross Barnett**- Affiliation: University of Waikato, Hamilton, New Zealand
- Email: arbus@math.waikato.ac.nz
- 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: https://doi.org/10.1090/S0025-5718-2011-02565-2
- MathSciNet review: 2904597