Answer by Jairo Bochi for Existence of algebraic integers with certain...
@orthodontist has already given a clean and educated answer to my question. Nevertheless let me include an elementary answer, tweaking Vijayaraghavan's construction. The calculations are not terribly...
View ArticleAnswer by orthodontist for Existence of algebraic integers with certain...
You can even construct such a polynomial for any totally real field $K$ of degree $n$. By Dirichlet's theorem, the unit group $U$ of $K$ maps to$$U \rightarrow (K^* \otimes \mathbf{R}) \stackrel{\log|...
View ArticleExistence of algebraic integers with certain properties
Is the following statement true?($\star$) Given integers $n > k > 0$, there exists a monic polynomial of degree $n$ with integer coefficients and constant term $\pm 1$, irreducible over...
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