Y. Tanigawa · wovepaper

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

11 papers

On a Turán's theorem for arithmetic progressions

T. Makoto Minamide, Haruka Sakai, Yoshio Tanigawa

Let $m \geq 1$ be a fixed integer, $a$ an integer satisfying $(a, m) = 1$ , and $z \geq 1$ a real parameter. Denote by $ω_{z} (n; m, a)$ the number of distinct prime divisors $p$ of $n$ sat…

On a Turán's theorem for small primes

T. Makoto Minamide, Haruka Sakai, Yoshio Tanigawa

Denote by $ω (n)$ the number of distinct prime divisors of the natural number $n$ . In 2007, Granville and Soundararajan gave a quite new method to compute the higher moments $\sum_{…

Continued fraction formulae involving ratios of three gamma functions

Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai

Via the MC-algorithm, in this paper we produce seven continued fraction formulae involving products and quotients of three gamma functions with three parameters, and another is an…

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(…

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

Continued fraction expression of the Mathieu series

Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai

In this paper, we represent a continued fraction expression of Mathieu series by a continued fraction formula of Ramanujan. As application, we obtain some new bounds for Mathieu se…

math.CA2015★ 1 cited

The fastest possible continued fraction approximations of a class of functions

Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai

The goal of this paper is to formulate a systematical method for constructing the fastest possible continued fraction approximations of a class of functions. The main tools are the…

math.NT2015★ 1 cited

Mean square of the error term in the asymmetric many dimensional divisor problem

Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai

Let $\ba=(a_1,a_2,\ldots,a_k)$, where $a_{j} (j = 1, \dots, k)$ are positive integers such that $a_{1} \leq a_{2} \leq \dots \leq a_{k}$ . Let $d(\ba;n)=\sum_{n_1^{a_1}\cdots n_k^{a_k}=n}1$…

math.NT2015★ 9 cited

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

Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai

In 1956, Tong established an asymptotic formula for the mean square of the error term in the summatory function of the Piltz divisor function $d_{3} (n) .$ The aim of this paper is to…

math.NT2008★ 8 cited

On the Rankin-Selberg problem: higher power moments of the Riesz mean error term

Yoshio Tanigawa, Wenguang Zhai, Deyu Zhang

Let $Δ_{1} (x; ϕ)$ be the error term of the first Riesz means of the Rankin-Selberg zeta function. We study the higher power moments of $Δ_{1} (x; ϕ)$ and derive an asymptotic formula for…

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…