Notes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large Primes
Year: 2026
Type: preprint
Abstract: As applications of non-standard analysis to the study of transcendence in the ring $\mathscr{A}$ of integers modulo infinitely large primes, we extend transcendence criteria by Anzawa--Funakura and Matsusaka--Seki. Using the extension of the criterion by Anzawa--Funakura, we observe conditional relation between asymptotic behaviour of prime gaps and transcendence in $\mathscr{A}$. We also summarise known algebraic and model theoretic results on $\mathscr{A}$ for number theorists, and share topics in transcendental number theory with algebraists and model theorists.
Source: arXiv (Cornell University)
Author: Mihara, Tomoki
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160110735