Zobrazeno 1 - 10
of 91
pro vyhledávání: '"Yoshio Tanigawa"'
Publikováno v:
Acta Arithmetica; 2024, Vol. 216 Issue 4, p291-327, 37p
Publikováno v:
The Ramanujan Journal. 58:597-631
Let $$k\geqslant 2$$ be a fixed natural number and $$d_k(n)$$ denote the number of ways n can be written as a product of k positive integers. We use $$\Delta _k(x)$$ to denote the error term in the asymptotic formula of the summatory function of $$d_
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0db5dce88b367591f9480c2e63acbcf8
https://doi.org/10.1007/s11139-021-00431-w
https://doi.org/10.1007/s11139-021-00431-w
Publikováno v:
Pacific Journal of Mathematics. 304:15-41
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::481314baff88781e4b99c087da623ad7
https://doi.org/10.2140/pjm.2020.304.15
https://doi.org/10.2140/pjm.2020.304.15
Publikováno v:
Canadian Journal of Mathematics. 71:1465-1493
Let $\unicode[STIX]{x1D701}(s)$ be the Riemann zeta function. In 1929, Hardy and Littlewood proved the approximate functional equation for $\unicode[STIX]{x1D701}^{2}(s)$ with error term $O(x^{1/2-\unicode[STIX]{x1D70E}}((x+y)/|t|)^{1/4}\log |t|)$, w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3057b90f91874e0f2f5fb497d5beae71
https://doi.org/10.4153/cjm-2018-004-9
https://doi.org/10.4153/cjm-2018-004-9
Publikováno v:
Research in Number Theory. 7
Let $$\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$$ . Furthermore we derive an upper bound for $$\in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::51bab7a1eb6dc82e90f25ba720389cfb
https://doi.org/10.1007/s40993-021-00255-z
https://doi.org/10.1007/s40993-021-00255-z
Publikováno v:
Tokyo Journal of Mathematics.
Lately, Kiuchi and Minamide studied the mean square of the double zeta-function $\zeta_2(\sigma_{1}+it_1, \sigma_{2}+it_2)$ with respect to $ t_1 $ in the critical region. In this paper, using a new upper bound of $\zeta_{2}(\sigma_{1}+it_1, \sigma_{
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::acaf23addf9f912244b1e7b53869cd1a
https://doi.org/10.3836/tjm/1502179322
https://doi.org/10.3836/tjm/1502179322
Publikováno v:
Acta Arithmetica.
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_{
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dc7d8ac202c9966b988ed16844e2a1cf
https://doi.org/10.4064/aa191103-13-2
https://doi.org/10.4064/aa191103-13-2
Publikováno v:
Hardy-Ramanujan Journal
Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2019, 41, pp.40-47
Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2019, 41, pp.40-47
The aim of this note is to establish a subclass of $\mathcal{F}$ considered by Segal if functions for which the Ingham-Wintner summability implies $\mathcal{F}$-summability as wide as possible. The subclass is subject to the estimate for the error te
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5ddbe1f980f395fd07679023cdc42ea2
https://doi.org/10.46298/hrj.2019.5104
https://doi.org/10.46298/hrj.2019.5104
Publikováno v:
Journal of the Australian Mathematical Society. 103:231-249
We attempt to discuss a new circle problem. Let $\unicode[STIX]{x1D701}(s)$ denote the Riemann zeta-function $\sum _{n=1}^{\infty }n^{-s}$ ($\text{Re}\,s>1$) and $L(s,\unicode[STIX]{x1D712}_{4})$ the Dirichlet $L$-function $\sum _{n=1}^{\infty }\unic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fa3f0fb47b1c8d6a3c23e55921c038e5
https://doi.org/10.1017/s1446788716000525
https://doi.org/10.1017/s1446788716000525
Publikováno v:
International Journal of Number Theory. 12:1675-1701
Let [Formula: see text] be a Dirichlet series in the Selberg class of degree [Formula: see text] and let [Formula: see text] be the arithmetical error term of [Formula: see text]. We derive two kinds of the mean square estimates of [Formula: see text
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::46ddbe9d0bbf8ebb02145b831874d542
https://doi.org/10.1142/s1793042116501037
https://doi.org/10.1142/s1793042116501037