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Results tagged with cyclotomic-fields
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user 3684
A cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to $\mathbb Q$, the field of rational numbers.
8
votes
which algebraic integers in a cyclotomic field give you integer absolute value?
What follows is not mine. It was posted by Scaroth, and then deleted by Scaroth, with the explanation, "Given the subsequent comments of the OP, the indication was that this answer was not even read, …
2
votes
When does the absolute value of a sum of an integer and an algebraic integer equal an integer?
Just to give a numerical example, if $\zeta=(1+i\sqrt3)/2$, a 6th root of unity, and $z=1+8\zeta=5+4i\sqrt3$, and $D=6$, then $z$ is a sum of roots of unity, $D$ is a rational integer, $|z+D|=|11+4i\s …
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4
votes
Accepted
Something interesting about the quintic $x^5 + x^4 - 4 x^3 - 3 x^2 + 3 x + 1=0$ and its cousins
I think the depressed quintic in the question is what Emma Lehmer called the reduced quintic in her paper, The quintic character of 2 and 3, Duke Math. J. Volume 18, Number 1 (1951), 11-18, MR0040338. …
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