Browsing by Author "Barnett, A. Ross"

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  • Corrigendum to "The holomorphic flow of the Riemann Zeta function"

    Broughan, Kevin A.; Barnett, A. Ross (American Mathematical Society, 2007)
    Theorem 4.5 of [2], describing the topological type of the zeros of the flow s˙ = ζ(s) at reflected points off the critical line, claiming they were the same, contains an error. We gratefully acknowledge Professor Cevat ...
  • Gram lines and the average of the real part of the Riemann zeta function

    Broughan, Kevin A.; Barnett, A. Ross (American Mathematical Society, 2011)
    The contours ξ Λ(s) = 0 of the function which satisfies ζ(1-s) = Λ(s)ζ(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 ...
  • The holomorphic flow of the Riemann zeta function

    Broughan, Kevin A.; Barnett, A. Ross (American Mathematical Society, 2003-11)
    The flow of the Riemann zeta function, ś = ς(s), is considered, and phase portraits are presented. Attention is given to the characterization of the flow lines in the neighborhood of the first 500 zeros on the critical ...
  • Linear law for the logarithms of the Riemann periods at simple critical zeta zeros

    Broughan, Kevin A.; Barnett, A. Ross (American Mathematical Society, 2006)
    Each simple zero 1/2 + iγn of the Riemann zeta function on the critical line with γn > 0 is a center for the flow s˙ = ξ(s) of the Riemann xi function with an associated period Tn. It is shown that, as γn →∞, log Tn ≥ π/4 ...
  • On the subsequence of primes having prime subscripts

    Broughan, Kevin A.; Barnett, A. Ross (University of Waterloo, 2009)
    We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimates for its counting function. We obtain bounds for the weighted gaps between elements of the subsequence and show that for ...

A. Ross Barnett has 2 co-authors in Research Commons.