Y. Tanigawa

activity

20082026

most citedOn the Tong-type identity and the mean square of the error term for an extended Selberg class

9 citations · 19 across the 11 of their papers we have counts for

collaborators

Showing 2020Show all

2 papers · 1 filter

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 $\int_{0}^{T} Z^{2} (t) ζ (1/2 + i t) d t$ .…