A new experimental and visual approach to the Riemann zeros

Key Points

• The research aims to explore a novel visual and experimental method for understanding the Riemann zeros.
• Decomposed integers into cyclic families of the form 2^k + c.
• Developed restricted zeta functions whose nontrivial zeros align on Re(s) = 1/2.
• Utilized spiral visualizations to illustrate intersections with Riemann zeros.
• Demonstrated that regularized sums can recover the traditional zeta function ζ(s).
• Found a common intersection point between spiral visualizations and the Riemann zeros.
• Established an explicit formula linking prime numbers to the zeros of the restricted zeta functions.