How to construct Weil numbers in a given CM quartic field? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T01:52:42Z http://mathoverflow.net/feeds/question/111235 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111235/how-to-construct-weil-numbers-in-a-given-cm-quartic-field How to construct Weil numbers in a given CM quartic field? Tommaso Centeleghe 2012-11-02T01:42:48Z 2012-11-02T01:42:48Z <p>Let $L$ be a CM field of degree $4$ over the rationals, and let $p$ be a prime number. If $q$ is a power of $p$, I would like to know if it is possible to characterize (in some way) all Weil ${\bf F}_q$-numbers inside $L$.</p> <p>I was inspired by the corresponding question when $L$ has absolute degree $2$ (i.e., it is an imaginary quadratic field), which has a simple answer: Weil $q$-numbers $\pi$, up to roots of unity in $L$, correspond to principal ideals of norm $q$. The answer in this case is especially simple to get because $L$ has only one archimedean place.</p> <p>How harder is the problem when $L$ is quartic? Thanks.</p>