2007/09/04 by S. K. Sekatskiǐ, Sekatskii, Sergey K. · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fusion and Plasma Physics Studies #Mathematical Physics (math-ph) #Scientific Research and Philosophical Inquiry #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.0709.0364
openalex publication_date 2007/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of construction of a simple one - dimensional Hamiltonian whose spectrum coincides with the set of primes is considered. We note that quasiclassically a Hamiltonian whose spectrum has the same counting function as that of the primes in the leading order (i. e. integral logarithm) can be constructed with the function V(x) whose inverse is asymptotically given by x=li(V^(1/2)). Hamiltonians, whose spectra coincide with the first 1 - 1000 primes are constructed numerically and their fractal structure is revealed. The possibility of using such a "prime-generating" Hamiltonian for investigation of certain number-theoretical problems is discussed.