Wataru Takeda

activity

20172020

collaborators

4 papers

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

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

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…