10 papers · 1 filter
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…
On Hardy's -function and its derivatives associated with the extended Selberg class
Hirotaka Kobayashi
Hardy's -function is a real-valued function of the real variable , and whose zeros correspond exactly to the zeros of the Riemann zeta-function on the critical line. I…
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 . It reveals noticeable relation b…
Counting relatively prime pairs of palindromes
Hirotaka Kobayashi, Yuta Suzuki, Ryota Umezawa
For a given base , a positive integer is called a palindrome if its base expansion reads the same backwards as forwards. In this paper, we give an asymptotic formula for…
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 . It shows that the first main term is…
On a generalisation of the Riemann -function
Hirotaka Kobayashi
It is known that we can construct the meromorphic function associated with the higher derivative of Hardy's -function. In this paper, we introduce the entire function d…