Hirotaka Kobayashi

activity

20182025

collaborators

10 papers

math.NT2025

Explicit extreme values of the argument of the Riemann zeta-function

Shōta Inoue, Hirotaka Kobayashi, Yuichiro Toma

We investigate explicit extreme values of the argument of the Riemann zeta-function in short intervals. As an application, we improve the result of Conrey and Turnage-Butterbaugh c…

math.NT2025

On Hardy's $Z$ -function and its derivatives associated with the extended Selberg class

Hirotaka Kobayashi

Hardy's $Z$ -function $Z (t)$ is a real-valued function of the real variable $t$ , and whose zeros correspond exactly to the zeros of the Riemann zeta-function on the critical line. I…

math.NT2023

Mean-square values of the Riemann zeta function on arithmetic progressions

Hirotaka Kobayashi

We obtain asymptotic formulae for the second discrete moments of the Riemann zeta function over arithmetic progressions $\frac{1}{2} + i (an + b)$ . It reveals noticeable relation b…

math.NT2023

Counting relatively prime pairs of palindromes

Hirotaka Kobayashi, Yuta Suzuki, Ryota Umezawa

For a given base $g \geq 2$ , a positive integer is called a palindrome if its base $g$ expansion reads the same backwards as forwards. In this paper, we give an asymptotic formula for…

math.NT2023

A mean-square value of the Riemann zeta function over an arithmetic progression

Hirotaka Kobayashi

We obtain an asymptotic formula for the second discrete moment of the Riemann zeta function over the arithmetic progression $\frac{1}{2} + in$ . It shows that the first main term is…

math.NT2021

On a generalisation of the Riemann $ξ$ -function

Hirotaka Kobayashi

It is known that we can construct the meromorphic function $Z_{k} (s)$ associated with the higher derivative of Hardy's $Z$ -function. In this paper, we introduce the entire function d…

math.NT2021

On the Discrete Mean of the higher Derivative of Hardy's $Z$ -Function

Hirotaka Kobayashi

Yıldırım obtained an asymptotic formula of the discrete moment of $∣ ζ (\frac{1}{2} + i t) ∣$ over the zero of the higher derivatives of Hardy's $Z$ -function. We give a generalization of…

math.NT2020

On a certain sum of the derivatives of Dirichlet $L$ -functions

Hirotaka Kobayashi

We consider a sum of the derivatives of Dirichlet $L$ -functions over the zeros of Dirichlet $L$ -functions. We give an asymptotic formula for the sum.

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

On the discrete mean of the derivative of Hardy's $Z$ -function

Hirotaka Kobayashi

Update: This result was obtained by Milinovich with a better error term. He used $ζ^{'} (s)$ , but we considered $Z^{'} (t)$ . We corrected a typo in the main theorem. We consider the sum of…

Explicit extreme values of the argument of the Riemann zeta-function

On Hardy's Z-function and its derivatives associated with the extended Selberg class

Mean-square values of the Riemann zeta function on arithmetic progressions

Counting relatively prime pairs of palindromes

A mean-square value of the Riemann zeta function over an arithmetic progression

On a generalisation of the Riemann ξ-function

On the Discrete Mean of the higher Derivative of Hardy's Z-Function

On a certain sum of the derivatives of Dirichlet L-functions

Transcendence of values of the iterated exponential function at algebraic points

On the discrete mean of the derivative of Hardy's Z-function

On Hardy's $Z$ -function and its derivatives associated with the extended Selberg class

On a generalisation of the Riemann $ξ$ -function

On the Discrete Mean of the higher Derivative of Hardy's $Z$ -Function

On a certain sum of the derivatives of Dirichlet $L$ -functions

On the discrete mean of the derivative of Hardy's $Z$ -function