2025/08/14 by Sawian Jaidee, Jaidee, Sawian, Patrick Moss +3
Computer Science · Mathematics · #37C25 #Advanced Combinatorial Mathematics #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory
paper · doi:10.48550/arxiv.2508.11054
openalex publication_date 2025/08/14 · openalex created_date 2026/02/12 · openalex updated_date 2026/07/28
We introduce the notions of local realizability at a prime and algebraic realizability of an integer sequence. After discussing this notion in general we consider it for the Euler numbers, the Bernoulli denominators, and the Bernoulli numerators. This gives, for example, a dynamical characterization of the Bernoulli regular primes. Algebraic realizability of the Bernoulli denominators is shown at every prime, giving a different perspective on the great diversity of congruences satisfied by this sequence. We show that the sequence of Euler numbers cannot be realized on a nilpotent group, which may explain why it is less hospitable to congruence hunting.