Number Theory

    

A "Good" Problem Equivalent to the Riemann Hypothesis

Authors: Warren D. Smith

We exhibit a sequence cn such that the convergence of ∑cnzn for all complex z with |z|<1 is equivalent to the Riemann Hypothesis. We argue that this particular RH-equivalent problem is "better" than most, or perhaps every, other RH-equivalent problem devised so far, in the sense that (we prove) there is a tremendous gap in behaviors of the cn if the RH is true versus if the RH is false.

Comments: This 1995 paper by me, heavily revised 2005, had been sitting on my web page but is now uploaded to vixra for archival purposes.

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[v1] 2026-06-20 03:03:07

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