11 citations · 19 across the 23 of their papers we have counts for
26 papers
Parallel Searching Method for Verifying Finiteness of Prime Numbers Presented as Specific Linear Combinations of Factorials
Tomoki Mihara
As a new approach to search a counterexample of variants of Kurepa's conjecture, we investigate a parallel searching method of prime numbers satisfying \begin{eqnarray*} \sum_{…
Transcendence of Montgomery Reduction Factor in the Ring of Integers Modulo Infinitely Large Primes
Tomoki Mihara
We prove the transcendence over of the image of Montgomery reduction factor in the ring of integers modulo infinitely large primes. Here, for an odd…
Transcendence of Tonelli--Shanks Power Modulo Infinitely Large Primes
Tomoki Mihara
For a prime number , we denote by the greatest odd divisor of . Tonelli--Shanks algorithm is a classical algorithm to compute a square root of a quadratic residue $n…
Generalisation of Baker's Forcing Method to Arbitrary Prime and NP-hardness of Several -adic Optimisations
Tomoki Mihara
G.\ D.\ Baker formulated a forcing method to interpret integer optimisation problem into -adic linear regression, and proved the NP-hardness of -adic linear regression. We ge…
Schneider--Teitelbaum Duality over a Non-spherically Complete Field
Tomoki Mihara
We formulate Schneider--Teitelbaum duality between wide classes of Banach -linear representations of and left -modules for a non-spherically complete field , e.…
-adic Linear Regression for Random Sampling with Digitwise Noise
Tomoki Mihara
We propose a new probabilistic algorithm of -adic linear regression for random sampling with digitwise noise. This includes a new probabilistic algorithm of modulo linear re…