Number Theory

    

The Zeroes of the Zeta Function Encode Rational Approximations of Pi

Authors: Ryan Hackbarth

In this paper, I present a formula for the zeroes of the Riemann Zeta Function and highlight their dependence on a rational integer ratio. I connect these ratios with a hyperbola reminiscent of Pell’s equation which approximates pi and provide a table of calculated ratios and their corresponding Zero. Finally, I demonstrate the requirement of the critical line at ½ in producing these integer approximations.

Comments: 2 Pages.

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Submission history

[v1] 2026-01-11 01:30:39

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