On certain mean values of the double zeta-function
In this paper we discuss three types of the mean values of the Euler double zeta function. In order to get results we introduce three approximate formulas for this function.
math.NT↗
arXiv subjects
Kaneaki Matsuoka
Publications and source records attributed to Kaneaki Matsuoka.
On the higher derivatives of Z(t) associated with the Riemann Zeta-Function
Let $Z(t)$ be the classical Hardy function in the theory of the Riemann zeta-function. The main result in this paper is that if the Riemann hypothesis is true then for any positive integer $n$ there exists a $t_{n}>0$ such that for $t>t_{n}$ the function $Z^{(n+1)}(t)$ has exactly one zero between consecutive zeros of $Z^{(n)}(t)$.
math.NT↗