Description

What if every integer possessed a hidden geometric structure, a quantum signature encoded in its divisors?

This work investigates the possibility that integers admit an intrinsic geometric structure derived from their divisor relationships. Rather than treating natural numbers solely as isolated discrete entities, it develops a framework in which divisor structure induces a well-defined geometric and informational organization. Using rigorous proofs supported by computational analysis, the treatise proposes a coherent geometric theory of arithmetic grounded in divisor-based constructions, with formal connections to concepts from quantum information theory.

For over 2,000 years, mathematicians have studied the divisor function d(n) as a simple counting tool. The Quantum Geometry of Numbers proves that d(n) is far more profound, it is the fundamental geometric invariant of integers when viewed as points in an infinite-dimensional Hilbert space.

Why this Book matters:

✓ Exact Mathematics: Every theorem proven rigorously (83 pages, 17 chapters, full appendices)
✓ Computationally Verified: Tables and code for n ≤ 10⁶
✓ Genuinely Novel: First geometric theory of ℕ based on divisor structure
✓ Interdisciplinary Bridge: Connects number theory, functional analysis, information theory, and quantum formalism
✓ Accessible Progression: From intuitive foundations to advanced results

Who should read this:

Pure mathematicians (number theorists, functional analysts, geometers) Applied mathematicians (kernel methods, computational number theory) Theoretical computer scientists (quantum algorithms, complexity theory) Physicists (quantum information, discrete geometry) Graduate students seeking cutting-edge research directions