取整函数 (Chinese Wikipedia)

Analysis of information sources in references of the Wikipedia article "取整函数" in Chinese language version.

refsWebsite

Global rank Chinese rank

8archive.org

6^th place

4^th place

2books.google.com

3^rd place

8^th place

2web.archive.org

1^st place

1wikipedia.org

low place

archive.org

Lemmermeyer 2000，§ 1.4, Ex. 1.32–1.33. Lemmermeyer, Franz. Reciprocity Laws: from Euler to Eisenstein. Berlin: Springer. 2000. ISBN 3-540-66957-4.
Hardy & Wright 1980，§§ 6.11–6.13. Hardy, G. H.; Wright, E. M. An Introduction to the Theory of Numbers (Fifth edition). Oxford: Oxford University Press. 1980. ISBN 978-0-19-853171-5.
Lemmermeyer 2000，第25頁. Lemmermeyer, Franz. Reciprocity Laws: from Euler to Eisenstein. Berlin: Springer. 2000. ISBN 3-540-66957-4.
Hardy & Wright 1980，§ 22.3. Hardy, G. H.; Wright, E. M. An Introduction to the Theory of Numbers (Fifth edition). Oxford: Oxford University Press. 1980. ISBN 978-0-19-853171-5.
Ribenboim 1996，第186頁 Ribenboim, Paulo. The New Book of Prime Number Records. New York: Springer. 1996. ISBN 0-387-94457-5.
Ribenboim 1996，第181頁. Ribenboim, Paulo. The New Book of Prime Number Records. New York: Springer. 1996. ISBN 0-387-94457-5.
Ribenboim 1996，第180頁（譯文）：「雖然該些公式毫不實用⋯⋯但邏輯學家希望清晰明白不同公理體系，如何推導出算術各方面，則或許與此有關⋯⋯」 Ribenboim, Paulo. The New Book of Prime Number Records. New York: Springer. 1996. ISBN 0-387-94457-5.
Hardy & Wright 1980，第344—345頁（譯文）：「若數 $\alpha$ 的準確值⋯⋯可以無關質數的方式表達，則該些公式之任一（或一切類似公式）的地位將截然不同。似乎沒有此種可能，但卻不能完全排除。」 Hardy, G. H.; Wright, E. M. An Introduction to the Theory of Numbers (Fifth edition). Oxford: Oxford University Press. 1980. ISBN 978-0-19-853171-5.

books.google.com

Crandall & Pomerance 2001，Ex. 1.3, p. 46，求和式的上限 $\infty$ 可以換成 $n$ 。尚有一個等價的表述： $n>1$ 為質數當且僅當 $\sum _{m=1}^{\lfloor {\sqrt {n}}\rfloor }\left(\left\lfloor {\frac {n}{m}}\right\rfloor -\left\lfloor {\frac {n-1}{m}}\right\rfloor \right)=1.$ Crandall, Richard; Pomerance, Carl. Prime Numbers: A Computational Perspective. New York: Springer. 2001 [2022-02-06]. ISBN 0-387-94777-9. （原始内容存档于2022-04-09）.
Crandall & Pomerance 2001，Ex. 1.4, p. 46. Crandall, Richard; Pomerance, Carl. Prime Numbers: A Computational Perspective. New York: Springer. 2001 [2022-02-06]. ISBN 0-387-94777-9. （原始内容存档于2022-04-09）.

web.archive.org

Crandall & Pomerance 2001，Ex. 1.3, p. 46，求和式的上限 $\infty$ 可以換成 $n$ 。尚有一個等價的表述： $n>1$ 為質數當且僅當 $\sum _{m=1}^{\lfloor {\sqrt {n}}\rfloor }\left(\left\lfloor {\frac {n}{m}}\right\rfloor -\left\lfloor {\frac {n-1}{m}}\right\rfloor \right)=1.$ Crandall, Richard; Pomerance, Carl. Prime Numbers: A Computational Perspective. New York: Springer. 2001 [2022-02-06]. ISBN 0-387-94777-9. （原始内容存档于2022-04-09）.
Crandall & Pomerance 2001，Ex. 1.4, p. 46. Crandall, Richard; Pomerance, Carl. Prime Numbers: A Computational Perspective. New York: Springer. 2001 [2022-02-06]. ISBN 0-387-94777-9. （原始内容存档于2022-04-09）.

wikipedia.org

en.wikipedia.org

Ronald Graham, Donald Knuth and Oren Patashnik（英语：Oren Patashnik）. "Concrete Mathematics". Addison-Wesley, 1999. Chapter 3, "Integer Functions".