Tomoki Mihara

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math.NT2026

Schneider--Teitelbaum Duality over a Non-spherically Complete Field

Tomoki Mihara

We formulate Schneider--Teitelbaum duality between wide classes of Banach $k$ -linear representations of $G$ and left $O_{k} [[G]]$ -modules for a non-spherically complete field $k$ , e.…

math.NT2026

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

Tomoki Mihara

As applications of non-standard analysis to the study of transcendence, we extend transcendence criteria by Anzawa--Funakura and Matsusaka--Seki. We also summarise known algebraic…

math.NT2026

$p$ -adic Character Neural Network

Tomoki Mihara

We propose a new frame work of $p$ -adic neural network. Unlike the original $p$ -adic neural network by S.\ Albeverio, A.\ Khrennikov, and B.\ Tirrozi using a family of characterist…

math.NT2026

Bounded Additive Relation and Application to Finite Multiple Zeta Values

Tomoki Mihara

We formulate an algebraic problem to find a generating system of a finite subset of an Abelian group with respect to linear relations whose coefficients are bounded by a constant,…

math.NT2026

$p$ -adic Principal Component Analysis

Tomoki Mihara

We formulate a $p$ -adic optimisation problem on matrix factorisation, and investigate a heuristic method for it analogous to PCA.

Schneider--Teitelbaum Duality over a Non-spherically Complete Field

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

p-adic Character Neural Network

Bounded Additive Relation and Application to Finite Multiple Zeta Values

p-adic Principal Component Analysis

$p$ -adic Character Neural Network

$p$ -adic Principal Component Analysis