7
votes
2answers
302 views

Number of ways to write an integer as a product of irreducibles

Is there any way to tell the number of distinct ways to factor $a\in\mathcal{O}_k$ (up to units, of course) when $k$ is not a PID? A simple investigation in $\mathbb{Q}(\sqrt{-5})$ with integer ring ...
7
votes
2answers
498 views

Quintic polynomial solution by Jacobi Theta function.

Does someone have a good and rigorous reference for the solution of quintic ploynomial equation with Jacobi Theta function, in English? Mathworld and Wikipedia don't give a good English reference, at ...
0
votes
0answers
167 views

Ring of Integers as subring with most irreducibles

Let $L$ be a number field. Is it possible to define its ring of integers $R$ by saying it's the subring with (in a fuzzy sense) the "most" irreducibles?