Tomoki Mihara

activity

20132026

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12 papers · 1 filter

math.NT2026

Transcendence of Tonelli--Shanks Power Modulo Infinitely Large Primes

Tomoki Mihara

For a prime number $p$ , we denote by $k_{p}$ the greatest odd divisor of $p - 1$ . Tonelli--Shanks algorithm is a classical algorithm to compute a square root of a quadratic residue $n…

cs.CC2026

Generalisation of Baker's Forcing Method to Arbitrary Prime and NP-hardness of Several $p$ -adic Optimisations

Tomoki Mihara

G.\ D.\ Baker formulated a forcing method to interpret integer optimisation problem into $2$ -adic linear regression, and proved the NP-hardness of $2$ -adic linear regression. We ge…

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.…

stat.CO2026

$p$ -adic Linear Regression for Random Sampling with Digitwise Noise

Tomoki Mihara

We propose a new probabilistic algorithm of $p$ -adic linear regression for random sampling with digitwise noise. This includes a new probabilistic algorithm of modulo $p$ linear re…

cs.LG2026

$p$ -adic Manifold Learning and Benchmark Tasks from Impartial Games

Tomoki Mihara

We introduce $p$ -adic manifold learning, propose an algorithm to solve it, and propose benchmark tasks from impartial games.

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 in the ring $A$ of integers modulo infinitely large primes, we extend transcendence criteria by Anz…

Transcendence of Tonelli--Shanks Power Modulo Infinitely Large Primes

Generalisation of Baker's Forcing Method to Arbitrary Prime and NP-hardness of Several p-adic Optimisations

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

p-adic Linear Regression for Random Sampling with Digitwise Noise

p-adic Manifold Learning and Benchmark Tasks from Impartial Games

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

Generalisation of Baker's Forcing Method to Arbitrary Prime and NP-hardness of Several $p$ -adic Optimisations

$p$ -adic Linear Regression for Random Sampling with Digitwise Noise

$p$ -adic Manifold Learning and Benchmark Tasks from Impartial Games