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Numbers & p-adics papers 9 papers
Mathematicians. Valuation theory and the p-adic and adelic programme, Bruhat-Tits trees and ultrametric geometry as mathematics, Ostrowski's theorem, numeral and radix systems, primes, arithmetic and algebraic structures, zeta and gamma functions.
Spectral analysis. Spectra, eigen-structures and bounds Tagged papers: 35.
Spectral Decomposition of the Bruhat–Tits Tree as a Candidate Origin of Particle Mass Hierarchies: Exact Radial Spectrum, Finite Truncations, Semigroup Tests, and a Falsification Analysis
The Bruhat–Tits tree $\mathcal{T}_p$ of $\mathbb{Q}_p$ is the infinite $(p+1)$-regular tree that serves as the bulk of $p$-adic AdS/CFT. We test the conjecture that a natural Laplacian on $\mathcal{T}_p$ — or the prime-indexed arithmetic of the tree — encodes Standard Model mass ratios. We compute,…
Discriminating the Arithmetic Cut: Matched-Level-Density Null Models for the Primon-Gas Specific Heat and Spectral Correlations
The arithmetic-statistics program reads the two exchange statistics of identical particles as two multiplicity rules on one integer lattice, and its published observable is the specific heat of the primon gas: a computable deviation from the smooth ideal gas at every sampled temperature. The…
Harmonic Analysis is Langlands — The Fast Fourier Transform as the Computational Langlands Correspondence for GL(1)
We identify the Fast Fourier Transform (FFT) as the computational Langlands correspondence for the general linear group GL(1). Harmonic analysis on the finite cyclic group Z/nZ decomposes functions into irreducible characters -- the FFT -- and this structure generalises directly to harmonic analysis…
Spectral Analysis of Anomalous Diffusion on p-Adic Fractals
The reconcilement of continuous Riemannian geometry with the discrete arithmetic of the integers remains one of the most profound challenges in mathematical physics, particularly regarding the spectral interpretation of the Riemann zeros (Berry & Keating, 1999). While standard diffusion on…
Spectral Dynamics on Bruhat-Tits Trees
The probabilistic nature of prevalent primality tests, such as Miller-Rabin, presents a fundamental limitation where certainty is achieved only asymptotically. This study proposes a deterministic alternative rooted in the non-Archimedean geometry of p-adic numbers, specifically leveraging the…
Prime Numbers as Spectral Artifacts
This establishes a mathematical framework demonstrating that prime numbers emerge as spectral artifacts from a continuous quantum geometric substrate, rather than representing fundamental discrete entities. Through formal deduction from five established mathematical facts—base-independence of…
Arithmetic Gauge Concentration
Analytic number theory traditionally relies on probabilistic models to describe the asymptotic distribution of prime numbers, treating them as independent random variables. However, this approach fails to account for the deterministic rigidity observed in ergodic theory and the spectral statistics…
Continuous Topology and Discrete Arithmetic
The tension between the discrete cardinality of prime numbers and the continuous geometry of the complex plane is reconciled by treating primes as spectral residues governed by the explicit formulae of the Riemann zeta function. Sequential enumeration provides a linear coordinate that obscures the…
Spectral Schism
Standard analytic number theory treats the Riemann zeros as eigenvalues of a Hermitian operator acting on a rigid symplectic manifold. However, the asymptotic diffraction spectrum of the prime numbers exhibits fluid-like Lebesgue measure rather than the crystalline Bragg peaks required for such a…
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