| viXra.org > Number Theory > viXra:2408.0059 |
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| viXra.org > Number Theory > viXra:2408.0059 |
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Number Theory |
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Authors: Bryce Petofi Towne
The Riemann Hypothesis asserts that all non-trivial zeros of the Riemann zeta function lie on the critical line ( Re(s) = frac{1}{2} ) in the complex plane. This paper explores an alternative geometric approach by analyzing the zeta function and its non-trivial zeros in polar coordinates. Transforming the problem into this framework reveals a natural symmetry about the polar axis, which corresponds to the critical line in Cartesian coordinates.We demonstrate that the (Xi(s)) function, a redefined version of the zeta function, retains the symmetry ( Xi(s) = Xi(1 - s) ) in polar coordinates, supporting the hypothesis that non-trivial zeros must lie on the critical line.This geometric perspective suggests a potential simplification in verifying the Riemann Hypothesis and offers new insights into the distribution of non-trivial zeros.
Comments: 31 Pages.
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[v1] 2024-08-15 09:50:08
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