arXiv subjects

Jun-ichi Tamura

Publications and source records attributed to Jun-ichi Tamura.

4 recordsLinked to original sources

arXiv2023

Arithmetical independence of certain uniform sets of algebraic integers

We study four (families of) sets of algebraic integers of degree less than or equal to three. Apart from being simply defined, we show that they share two distinctive characteristics: almost uniformity and arithmetical independence. Here, ``almost uniformity'' means that the elements of a finite set are distributed almost equidistantly in the unit interval, while ``arithmetical independence'' means that the number fields generated by the elements of a set do not have a mutual inclusion relation each other. Furthermore, we reveal to what extent the algebraic number fields generated by the elements of the four sets can cover quadratic or cubic fields.

math.NT↗

arXiv2019

Multidimensional $p$-adic continued fraction algorithms

We give a new class of multidimensional $p$-adic continued fraction algorithms. We propose an algorithm in the class for which we can expect that multidimensional $p$-adic version of Lagrange's Theorem holds.

math.NT↗

arXiv2017

Continued fraction algorithms and Lagrange's theorem in ${\mathbb Q}_p$

We present several continued fraction algorithms, each of which gives an eventually periodic expansion for every quadratic element of ${\mathbb Q}_p$ over ${\mathbb Q}$ and gives a finite expansion for every rational number. We also give, for each of our algorithms, the complete characterization of elements having purely periodic expansions.

math.NT↗

arXiv2013

A new multidimensional slow continued fraction algorithm and stepped surface

We give a new algorithm of slow continued fraction expansion related to any real cubic number field as a 2-dimensional version of the Farey map. Using our algorithm, we can find the generators of dual substitutions (so-called tiling substitutions) for any stepped surface for any cubic direction.

math.NT↗