翻訳と辞書 Words near each other ・ Divya Ajith Kumar ・ Divya Bharti ・ Divya Bhaskar ・ Divya Deepa Charitable Trust ・ Divya Desam ・ Divya Dhar ・ Divya Dutta ・ Divya Gopalan ・ Divya Himachal ・ Divya Jyoti Higher Secondary School ・ Divya Khosla Kumar ・ Divya Kumar (singer) ・ Divya Narendra ・ Divya Nidhi Sharma ・ Divisor function ・ Divisor summatory function ・ Divisor topology ・ Divisoria LRT Station ・ Divisumma 18 ・ Divisão de Elite ・ Divisópolis ・ Divitas Networks ・ Divitdar Mehmed Emin Pasha ・ Divitz-Spoldershagen ・ Divizia A1 (Volei Feminin) ・ Divizia A1 (Volei Masculin) ・ Divizia Națională (disambiguation) ・ Divič ・ Divičani ・ Diviš Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Divisor summatory function ： ウィキペディア英語版 Divisor summatory function In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic behaviour of the Riemann zeta function. The various studies of the behaviour of the divisor function are sometimes called divisor problems. ==Definition== The divisor summatory function is defined as :$D(x)=\backslash sum\_\; d(n)\; =\; \backslash sum\_\; 1$ where :$d(n)=\backslash sigma\_0(n)\; =\; \backslash sum\_\; 1$ is the divisor function. The divisor function counts the number of ways that the integer ''n'' can be written as a product of two integers. More generally, one defines :$D\_k(x)=\backslash sum\_\; d\_k(n)=\backslash sum\_\; d\_(n)$ where ''d''''k''(''n'') counts the number of ways that ''n'' can be written as a product of ''k'' numbers. This quantity can be visualized as the count of the number of lattice points fenced off by a hyperbolic surface in ''k'' dimensions. Thus, for ''k''=2, ''D''(''x'') = ''D''2(''x'') counts the number of points on a square lattice bounded on the left by the vertical-axis, on the bottom by the horizontal-axis, and to the upper-right by the hyperbola ''jk'' = ''x''. Roughly, this shape may be envisioned as a hyperbolic simplex. This allows us to provide an alternative expression for ''D''(''x''), and a simple way to compute it in $O(\backslash sqrt)$ time: :$D(x)=\backslash sum\_^x\; \backslash left\backslash lfloor\backslash frac\backslash right\backslash rfloor\; =\; 2\; \backslash sum\_^u\; \backslash left\backslash lfloor\backslash frac\backslash right\backslash rfloor\; -\; u^2$, where $u\; =\; \backslash left\backslash lfloor\; \backslash sqrt\backslash right\backslash rfloor$ If the hyperbola in this context is replaced by a circle then determining the value of the resulting function is known as the Gauss circle problem. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Divisor summatory function」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.