The Golden Inversion: Primes as Projection from the Geometry of Q(√5)

University of Southampton

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Abstract

The golden zeta function (Paper 150) reproduces all 100 Riemann zeros tested using only the golden ratio φ, the golden norm √5, and summation — with no primes, no Euler product, and no sieve as input. Inserted into Riemann's explicit formula, the golden zeros count primes to within √x × 0.02. This inverts the standard relationship between primes and the zeta function: instead of primes → Euler product → ζ(s) → zeros → prime distribution, the chain runs φ → golden zeta → zeros → primes. We examine the consequences of this inversion. If primes are the multiplicative projection of the ideal lattice of ℤ[φ], then the prime number theorem is a geometric theorem about Q(√5), the Riemann hypothesis is a statement…

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Topics & keywords

Keywords
  • Multiplicative function
  • Riemann zeta function
  • Riemann hypothesis
  • Number theory
  • Multiplicative number theory
  • Euler's formula
  • Prime number theorem
  • Ideal (ethics)
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