YTYoshio Tanigawa
Yoshio Tanigawa
*This is an algorithmically generated author record based on publicly available information.
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Yoshio Tanigawa has a total of 32 co-authors. Here are the top co-authors by number of shared publications:
- Wenguang Zhai
Department of Mathematics, China University of Mining and Technology, Beijing 100083, P. R. China
13 shared publications - Xiaodong Cao
Department of Mathematics and Physics, Beijing Institute of Petro-Chemical Technology, Beijing, People’s Republic of China
11 shared publications - Shigeru Kanemitsu
Mathematical Research Center, Shandong University, 5 Hongjialou Road, Jinan 250100, China
8 shared publications - T. Makoto Minamide
Yamaguchi Univ, Grad Sch Sci & Technol Innovat, Yoshida 1677-1, Yamaguchi 7538512, Japan
5 shared publications - Jun Furuya
Okinawa National College of Technology
3 shared publications - Jun Furuya
Department of Integrated and Human Sciences (Mathematics), Hamamatsu University School of Medicine, Hamamatsu, Japan
3 shared publications
Latest Publications
- Open Access
On the higher moments of the error term in the Rankin-Selberg problem
Let $Δ_1(x;\varphi)$ denote the error term in the classical Rankin-Selberg problem. In this paper, we consider the higher power moments of $Δ_1(x;\varphi)$ and derive the asymptotic formulas for 3-rd, 4-th and 5-th power moments, which improve the previous results.Open AccessOn the higher moments of the error term in the Rankin-Selberg problem
Let $Δ_1(x;\varphi)$ denote the error term in the classical Rankin-Selberg problem. In this paper, we consider the higher power moments of $Δ_1(x;\varphi)$ and derive the asymptotic formulas for 3-rd, 4-th and 5-th power moments, which improve the previous results. - 11 April 2025
- Published by Institute of Mathematics, Czech Academy of Sciences
- Vol. 75 (2) , 485-518
On general Dedekind sums
Institute of Mathematics of the Czech Academy of Sciences
- 11 April 2025
- Published by Institute of Mathematics, Czech Academy of Sciences
- Vol. 75 (2) , 485-518
On general Dedekind sums
Institute of Mathematics of the Czech Academy of Sciences
- Open AccessOn the sum of $Δ_{k}(n)$ in the Piltz divisor problem for $k=3$ and $k=4$Let $Δ_{k}(x)$ be the error term in the classical asymptotic formula for the sum $\sum_{n\leq x}d_{k}(n)$, where $d_{k}(n)$ is the number of ways $n$ can be written as a product of $k$ factors. We study the analytic properties of the Dirichlet series $\sum_{n=1}^{\infty}Δ_{k}(n)n^{-s}$ and use Perron's formula to estimate the sums $\sum_{n\leq x}Δ_{3}(n)$ and $\sum_{n\leq x}Δ_{4}(n)$ for large $x>0$.Open AccessOn the sum of $Δ_{k}(n)$ in the Piltz divisor problem for $k=3$ and $k=4$Let $Δ_{k}(x)$ be the error term in the classical asymptotic formula for the sum $\sum_{n\leq x}d_{k}(n)$, where $d_{k}(n)$ is the number of ways $n$ can be written as a product of $k$ factors. We study the analytic properties of the Dirichlet series $\sum_{n=1}^{\infty}Δ_{k}(n)n^{-s}$ and use Perron's formula to estimate the sums $\sum_{n\leq x}Δ_{3}(n)$ and $\sum_{n\leq x}Δ_{4}(n)$ for large $x>0$.
- 1 January 2024
- Published by Institute of Mathematics, Polish Academy of Sciences in Acta Arithmetica
- Vol. 216 (4) , 291-327
On the sum of $\varDelta_k(n)$ in the Piltz divisor problem for $k=3$ and $k=4$Let $\Delta _k(x)$ be the error term in the classical asymptotic formula for the sum $\sum_{n \leq x}d_k(n)$, where $d_k(n)$ is the number of ways $n$ can be written as a product of $k$ factors. We study the analytic properties of the Dirichlet series $\s- 1 January 2024
- Published by Institute of Mathematics, Polish Academy of Sciences in Acta Arithmetica
- Vol. 216 (4) , 291-327
On the sum of $\varDelta_k(n)$ in the Piltz divisor problem for $k=3$ and $k=4$Let $\Delta _k(x)$ be the error term in the classical asymptotic formula for the sum $\sum_{n \leq x}d_k(n)$, where $d_k(n)$ is the number of ways $n$ can be written as a product of $k$ factors. We study the analytic properties of the Dirichlet series $\s- 17 May 2021
- Published by Springer Nature in The Ramanujan Journal
- Vol. 58 (2) , 597-631
On hybrid moments of $\Delta _2(x)$ and $\Delta _3(x)$- 17 May 2021
- Published by Springer Nature in The Ramanujan Journal
- Vol. 58 (2) , 597-631
On hybrid moments of $\Delta _2(x)$ and $\Delta _3(x)$- 16 April 2021
- Published by Springer Nature in Research in Number Theory
- Vol. 7 (2) , 1-16
Some mean value results related to Hardy’s function
- 16 April 2021
- Published by Springer Nature in Research in Number Theory
- Vol. 7 (2) , 1-16
Some mean value results related to Hardy’s function
- 1 January 2021
- Published by Institute of Mathematics, Polish Academy of Sciences in Acta Arithmetica
- Vol. 199 (3) , 237-251
Average of Hardy’s function at Gram points
Let $Z(t)=\chi ^{-1/2}(1/2+it)\zeta (1/2+it)=e^{i\theta (t)}\zeta (1/2+it)$ be Hardy’s function and $g(n)$ be the $n$th Gram point defined by $\theta (g(n))=\pi n$. Titchmarsh proved that $$ \sum _{n \leq N} Z(g(2n)) =2N+O(N^{3/4}\log ^{3/4}N) $$ and $$ \- 1 January 2021
- Published by Institute of Mathematics, Polish Academy of Sciences in Acta Arithmetica
- Vol. 199 (3) , 237-251
Average of Hardy’s function at Gram points
Let $Z(t)=\chi ^{-1/2}(1/2+it)\zeta (1/2+it)=e^{i\theta (t)}\zeta (1/2+it)$ be Hardy’s function and $g(n)$ be the $n$th Gram point defined by $\theta (g(n))=\pi n$. Titchmarsh proved that $$ \sum _{n \leq N} Z(g(2n)) =2N+O(N^{3/4}\log ^{3/4}N) $$ and $$ \- 1 May 2020
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 485 (1) , 123772
Mean square of the derivatives of Hardy's Z-function
- 1 May 2020
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 485 (1) , 123772
Mean square of the derivatives of Hardy's Z-function
- Open Access
Average of Hardy's function at Gram points
Let $Z(t)=\chi^{-1/2}(1/2+it)\zeta(1/2+it)=e^{i\theta(t)}\zeta(1/2+it)$ be Hardy's function and $g(n)$ be the $n$-th Gram points defined by $\theta(g(n))=\pi n$. Titchmarsh proved that $\sum_{n \leq N} Z(g(2n)) =2N+O(N^{3/4}\log^{3/4}N) $ and $\sum_{n \leq N} Z(g(2n+1)) =-2N+O(N^{3/4}\log^{3/4}N)$. We shall improve the error terms to $O(N^{1/4}\log^{3/4}N \log\log N)$.Open AccessAverage of Hardy's function at Gram points
Let $Z(t)=\chi^{-1/2}(1/2+it)\zeta(1/2+it)=e^{i\theta(t)}\zeta(1/2+it)$ be Hardy's function and $g(n)$ be the $n$-th Gram points defined by $\theta(g(n))=\pi n$. Titchmarsh proved that $\sum_{n \leq N} Z(g(2n)) =2N+O(N^{3/4}\log^{3/4}N) $ and $\sum_{n \leq N} Z(g(2n+1)) =-2N+O(N^{3/4}\log^{3/4}N)$. We shall improve the error terms to $O(N^{1/4}\log^{3/4}N \log\log N)$. - Open Access
Some mean value results related to Hardy's function
Let $\zeta(s)$ and $Z(t)$ be the Riemann zeta function and Hardy's function respectively. We show asymptotic formulas for $\int_0^T Z(t)\zeta(1/2+it)dt$ and $\int_0^T Z^2(t) \zeta(1/2+it)dt$. Furthermore we derive an upper bound for $\int_0^T Z^3(t)\chi^{\alpha}(1/2+it)dt$ for $-1/2<\alpha<1/2$, where $\chi(s)$ is the function which appears in the functional equation of the Riemann zeta function: $\zeta(s)=\chi(s)\zeta(1-s)$.Open AccessSome mean value results related to Hardy's function
Let $\zeta(s)$ and $Z(t)$ be the Riemann zeta function and Hardy's function respectively. We show asymptotic formulas for $\int_0^T Z(t)\zeta(1/2+it)dt$ and $\int_0^T Z^2(t) \zeta(1/2+it)dt$. Furthermore we derive an upper bound for $\int_0^T Z^3(t)\chi^{\alpha}(1/2+it)dt$ for $-1/2<\alpha<1/2$, where $\chi(s)$ is the function which appears in the functional equation of the Riemann zeta function: $\zeta(s)=\chi(s)\zeta(1-s)$.