Timeline for What is the probability that two numbers are relatively prime?
Current License: CC BY-SA 4.0
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| Oct 15, 2022 at 11:09 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken link fixed, cf. https://math.meta.stackexchange.com/a/34713/228959
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| May 16, 2012 at 4:09 | vote | accept | Owen Sizemore | ||
| May 16, 2012 at 1:26 | comment | added | Noam D. Elkies | ...... likewise $1/\zeta_K(n)$ is the probability that $n>1$ ideals or field elements have no common factor. This also lets you asymptotically count rational points up to a given height in projective space over $K$. Here's why I had to look up these references some years ago: arxiv.org/pdf/math/0104115v1.pdf | |
| May 16, 2012 at 1:24 | comment | added | Noam D. Elkies | A reference for the general "less commonly known fact" is Schanuel, S.H.: Heights in number fields, Bull. Soc. Math. France 107 (1979), 433–449. It is true also using field elements in place of ideals. A function-field analogue was announced by Serre in Lectures on the Mordell-Weil Theorem (F. Vieweg & Sohn, Braunschweig 1989) and proved independently but in the same way by S.DiPippo (Spaces of Rational Functions on Curves Over Finite Fields, Ph.D. Thesis, Harvard, 1990) and D.Wan (Heights and Zeta Functions in Function Fields, in The Arithmetic of Function Fields (1992)... | |
| May 15, 2012 at 20:14 | history | answered | Gjergji Zaimi | CC BY-SA 3.0 |