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David Loeffler
David Loeffler
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Given two randomly chosen positive rational integers, the probability that the two numbers are coprime is $\frac{6}{\pi^2}$, (it. This is also the probability that a positive integer is squarefree). There areAre there generalizations of these results for Gaussian integers? OrOr more generally for the ring of integers in an Algebraic Number Fieldalgebraic number field?

Given two randomly chosen positive rational integers, the probability that the two numbers are coprime is $\frac{6}{\pi^2}$, (it is also the probability that a positive integer is squarefree). There are generalizations of these results for Gaussian integers? Or more generally for the ring of integers in an Algebraic Number Field?

Given two randomly chosen positive rational integers, the probability that the two numbers are coprime is $\frac{6}{\pi^2}$. This is also the probability that a positive integer is squarefree. Are there generalizations of these results for Gaussian integers? Or more generally for the ring of integers in an algebraic number field?

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zacarias
zacarias
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Probability in the Primes

Given two randomly chosen positive rational integers, the probability that the two numbers are coprime is $\frac{6}{\pi^2}$, (it is also the probability that a positive integer is squarefree). There are generalizations of these results for Gaussian integers? Or more generally for the ring of integers in an Algebraic Number Field?