Number Theory

   

Analyzing Non-Trivial Zeros of the Riemann Zeta Function Using Polar Coordinates

Authors: Bryce Petofi Towne

This paper presents an approach to analyzing the non-trivial zeros of the Riemann zeta function using polar coordinates. We investigate whether the real part of all non-trivial zeros can be determined to be a constant value. By transforming the traditional complex plane into a polar coordinate system, we recalculated and examined several known non-trivial zeros of the zeta function. Our findings provide an alternative framework for understanding this profound mathematical conjecture.Through mathematical proof and leveraging analytic continuation and holomorphic function theory, we explore the nature of (sigma) in the polar coordinate system. This analysis transforms the problem into a geometric one, allowing for simpler and more intuitive calculations. This approach provides a step towards an alternative understanding of the properties of the Riemann zeta function's non-trivial zeros. The findings of this work indicates that wit this geometric perspective, the Riemann Hypothesis holds true.

Comments: 22 Pages.

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Submission history

[v1] 2024-06-14 21:18:15
[v2] 2024-06-19 17:46:17
[v3] 2024-07-19 05:10:24

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