Wataru Takeda

activity

20162026

most citedVisible lattice points and the Extended Lindelöf Hypothesis

8 citations · 28 across the 15 of their papers we have counts for

collaborators

15 papers

math.NT2026

Simultaneous visibility in the algebraic lattice

Rishi Kumar, Wataru Takeda

Let $K$ be a number field with ring of integers $O$ . Two lattice points $x, y \in O^{m}$ with $m \geq 2$ are said to be visible from one another if $\gcd((x_i…

math.NT2023

On the Bhargava factorial of polynomial maps

Wataru Takeda

Bhargava introduced a generalization of the factorial function to extend classical results in integers to Dedekind rings and unify them. We study the Bhargava factorial of the imag…

math.NT2022

An interpolation of the generalized duality formula for the Schur multiple zeta values to complex functions

Maki Nakasuji, Yasuo Ohno, Wataru Takeda

One of the important research subjects in the study of multiple zeta functions is to clarify the linear relations and functional equations among them. The Schur multiple zeta funct…

math.NT2022

Shuffle product formula of the Schur multiple zeta values of hook type

Maki Nakasuji, Wataru Takeda

We discuss the shuffle product of the Schur multiple zeta values, which are the special values of Schur multiple zeta functions. We first define $2$ -labeled Schur posets to general…

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★ 4 cited

The Pieri formulas for hook type Schur multiple zeta functions

Maki Nakasuji, Wataru Takeda

We study the Pieri type formulas for the Schur multiple zeta functions along with those for the Schur polynomials. To formulate these formulas, we introduce a new insertion rule fo…

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.NT2019★ 5 cited

On the finiteness of solutions for polynomial-factorial Diophantine equations

Wataru Takeda

We study the Diophantine equations obtained by equating a polynomial and the factorial function, and prove the finiteness of integer solutions under certain conditions. For example…

math.NT2018★ 4 cited

Finiteness of trivial solutions of factorial products yielding a factorial over number fields

Wataru Takeda

We consider a Bertrand type estimate for primes splitting completely. As one of its applications, we show the finiteness of trivial solutions of Diophantine equation about the fact…

math.NT2018★ 4 cited

Uniform bounds of Piltz divisor problem over number fields

Wataru Takeda

We consider the upper bound of Piltz divisor problem over number fields. Piltz divisor problem is known as a generalization of the Dirichlet divisor problem. We deal with this prob…

math.NT2017

Uniform upper bounds of the distribution of relatively r-prime lattice points

Wataru Takeda

We estimate the distribution of relatively $r$ -prime lattice points in number fields $K$ with their components having a norm less than $x$ . In the previous paper we obtained unifor…

math.NT2017★ 1 cited

The distribution of lattice points with relatively r-prime

Wataru Takeda

The distribution of lattice points with relatively $r$ -prime is related to problems in the Number Theory such as the Extended Lindelöf Hypothesis and the Gauss Circle Problem. It i…

math.NT2016★ 8 cited

Visible lattice points and the Extended Lindelöf Hypothesis

Wataru Takeda

We consider the number of visible lattice points under the assumption of the Extended Lindelöf Hypothesis. We get a relation between visible lattice points and the Extended Lindelö…

math.NT2016

The number of relatively $r$ -prime $k$ -tuple integers

Wataru Takeda

For a fixed integer $r \geq 1$ , we say $k$ -tuple integers $(x_{1}, \dots, x_{k})$ are relatively $r$ -prime if there exists no prime $p$ such that all $k$ integers is multiple of $p^{r}$ . Ben…

math.NT2016★ 1 cited

The exact order of the number of lattice points visible from the origin

Wataru Takeda

We say a lattice point $X = (x_{1}, \dots, x_{m})$ is visible from the origin, if $g cd (x_{1}, ..., x_{m}) = 1$ . In other word, there are no other lattice point on the line segment from the origi…

Simultaneous visibility in the algebraic lattice

On the Bhargava factorial of polynomial maps

An interpolation of the generalized duality formula for the Schur multiple zeta values to complex functions

Shuffle product formula of the Schur multiple zeta values of hook type

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

The Pieri formulas for hook type Schur multiple zeta functions

Transcendence of values of the iterated exponential function at algebraic points

On the finiteness of solutions for polynomial-factorial Diophantine equations

Finiteness of trivial solutions of factorial products yielding a factorial over number fields

Uniform bounds of Piltz divisor problem over number fields

Uniform upper bounds of the distribution of relatively r-prime lattice points

The distribution of lattice points with relatively r-prime

Visible lattice points and the Extended Lindelöf Hypothesis

The number of relatively r-prime k-tuple integers

The exact order of the number of lattice points visible from the origin

The number of relatively $r$ -prime $k$ -tuple integers