Y. Tanigawa

collaborators

3 papers

math.NT2020

Average of Hardy's function at Gram points

Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai

Let $Z (t) = χ^{- 1/2} (1/2 + i t) ζ (1/2 + i t) = e^{i θ (t)} ζ (1/2 + i t)$ be Hardy's function and $g (n)$ be the $n$ -th Gram points defined by $θ (g (n)) = π n$ . Titchmarsh proved that $\sum_{n \leq N} Z(…

math.NT2020

Some mean value results related to Hardy's function

Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai

Let $ζ (s)$ and $Z (t)$ be the Riemann zeta function and Hardy's function respectively. We show asymptotic formulas for $\int_{0}^{T} Z (t) ζ (1/2 + i t) d t$ and $\int_{0}^{T} Z^{2} (t) ζ (1/2 + i t) d t$ .…

math.NT2008

On the fourth power moment of $Δ (x)$ and $E (x)$ in short intervals

Yoshio Tanigawa, Wenguang Zhai

Let $Δ (x)$ and $E (x)$ be error terms of the sum of divisor function and the mean square of the Riemann zeta function, respectively. In this paper their fourth power moments for sho…

Average of Hardy's function at Gram points

Some mean value results related to Hardy's function

On the fourth power moment of Δ(x) and E(x) in short intervals

On the fourth power moment of $Δ (x)$ and $E (x)$ in short intervals