A particular linear combination of the Riemann zeta function and its derivatives and the fraction of the Riemann zeta zeros on the critical line

We will introduce a particular linear combination of the Riemann zeta func-tion and its derivatives that satisfies a translation functional equation and discuss the role of this construction and related problems in an approach to the problem of getting a lower bound on the fraction of the zeros of the Riemann zeta function on the critical line. This is work in progress with T.A. Preobrazhenskaya.

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