5 papers
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 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…
On the Discrete Mean of the higher Derivative of Hardy's -Function
Hirotaka Kobayashi
Yıldırım obtained an asymptotic formula of the discrete moment of over the zero of the higher derivatives of Hardy's -function. We give a generalization of…
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 is the minimum of positive integers such that is rational. In this paper, we show that the number of algebraic numbers $A…
On the discrete mean of the derivative of Hardy's -function
Hirotaka Kobayashi
Update: This result was obtained by Milinovich with a better error term. He used , but we considered . We corrected a typo in the main theorem. We consider the sum of…