Kota Saito

activity

20172023

most citedApproximate Expected Utility Rationalization

4 citations · 13 across the 17 of their papers we have counts for

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10 papers · 1 filter

math.NT2023

Finiteness of solutions to linear Diophantine equations on Piatetski-Shapiro sequences

Kota Saito

A sequence of integers of the form $⌊ n^{α} ⌋$ $(n = 1, 2, \dots)$ for some fixed non-integral $α > 1$ is called a Piatetski-Shapiro sequence, where $⌊ x ⌋$ denotes…

math.NT2022

A system of certain linear Diophantine equations on analogs of squares

Yuya Kanado, Kota Saito

This study investigates the existence of tuples $(k, ℓ, m)$ of integers such that all of $k$ , $ℓ$ , $m$ , $k + ℓ$ , $ℓ + m$ , $m + k$ , $k + ℓ + m$ belong to $S (α)$ , where $S (α)$ i…

math.NT2021★ 1 cited

Topological properties and algebraic independence of sets of prime-representing constants

Kota Saito, Wataru Takeda

Let $(c_{k})_{k \in N}$ be a sequence of positive integers. We investigate the set of $A > 1$ such that the integer part of $A^{c_{1} \dots c_{k}}$ is always a prime number for eve…

math.NT2021

Prime-representing functions and Hausdorff dimension

Kota Saito

In 2010, Matomäki investigated the set of $A > 1$ such that the integer part of $A^{c^{k}}$ is a prime number for every $k \in N$ , where $c \geq 2$ is any fixed real number. S…

math.NT2020

Linear equations with two variables in Piatetski-Shapiro sequences

Kota Saito

For every non-integral $α > 1$ , the sequence of the integer parts of $n^{α}$ $(n = 1, 2, \dots)$ is called the Piatetski-Shapiro sequence with exponent $α$ , and let $PS (α)$ denot…

math.NT2020★ 1 cited

Linear Diophantine equations in Piatetski-Shapiro sequences

Toshiki Matsusaka, Kota Saito

A Piatetski-Shapiro sequence with exponent $α$ is a sequence of integer parts of $n^{α}$ $(n = 1, 2, \dots)$ with a non-integral $α > 0$ . We let $PS (α)$ denote the set of thos…

math.NT2020★ 2 cited

Distributions of Finite Sequences Represented by Polynomials in Piatetski-Shapiro Sequences

Kota Saito, Yuuya Yoshida

By using the work of Frantzikinakis and Wierdl, we can see that for all $d \in N$ , $α \in (d, d + 1)$ , and integers $k \geq d + 2$ and $r \geq 1$ , there exist infinitely many $n\in\math…

math.NT2020

Transcendence of values of the iterated exponential function at algebraic points

Hirotaka Kobayashi, Kota Saito, Wataru Takeda

We say that the order of an algebraic number $A$ is the minimum of positive integers $k$ such that $A^{k}$ is rational. In this paper, we show that the number of algebraic numbers $A…

math.NT2018★ 2 cited

Arithmetic Progressions in the Graphs of Slightly Curved Sequences

Kota Saito, Yuuya Yoshida

A strictly increasing sequence of positive integers is called a slightly curved sequence with small error if the sequence can be well-approximated by a function whose second deriva…

math.NT2018

New fractal dimensions and some applications to arithmetic patches

Kota Saito

In this paper, we define new fractal dimensions of a metric space in order to calculate the roughness of a set on a large scale. These fractal dimensions are called upper zeta dime…