2024/09/26 by Daniel Mayer, Mayer, Daniel C., Nicuşor Minculete +5
Computer Science · Mathematics · #11A25 #11A51 #11R11 #11R29 #11R37 #20D15 #47B06 #94A17 #Advanced Mathematical Identities #Analytic Number Theory Research #Computability, Logic, AI Algorithms #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #Primary: 28D20 #Secondary: 11S15
paper · pdf · doi:10.48550/arxiv.2409.18229
openalex publication_date 2024/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain inequalities involving the entropy of a positive integer and the divergence of two positive integers, respectively the entropy of an ideal and the divergence of two ideals in a ring of algebraic integers. Among the important results, we show that the minimal entropy arises for sharp localization, and the maximal entropy occurs for equidistribution. We also study other interesting estimates of entropy and divergence for numbers and for ideals. Finally, we determine the entropies of probability distributions on infinite trees of Schur σ-groups, which are realized by 3-class field tower groups of imaginary quadratic number fields.