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arXiv · 2605.00512

Notes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large Primes

Tomoki Mihara
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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.

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Tomoki Mihara. 2026-05-01. Notes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large Primes. https://arxiv.org/abs/2605.00512

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