Gram lines and the average of the real part of the Riemann zeta function

Authors:
Kevin A. Broughan and A. Ross Barnett

Journal:
Math. Comp. **81** (2012), 1669-1679

MSC (2010):
Primary 11M06

DOI:
https://doi.org/10.1090/S0025-5718-2011-02565-2

Published electronically:
December 7, 2011

MathSciNet review:
2904597

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Abstract | References | Similar Articles | Additional Information

Abstract: The contours of the function which satisfies

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 is imaginary. When suitably averaged the real part of satisfies a relation which greatly extends a theorem of Titchmarsh, (namely that the average of over the Gram points has the value 2), to the open right-hand half plane .

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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

DOI:
https://doi.org/10.1090/S0025-5718-2011-02565-2

Keywords:
Gram points,
Gram lines,
Riemann zeta function

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

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.