Denominators of algebraic numbers in a number field

TextFor any algebraic number γ  , let g(x)g(x) be the unique irreducible polynomial with integral coefficients, whose leading coefficient c(γ)c(γ) is positive, such that g(γ)=0g(γ)=0. Let d(γ)d(γ) be the denominator of γ. We fix a number field K, a prime p, a positive integer k   and we study the set of values of vp(c(γ))vp(c(γ)), when γ runs in the set of the primitive elements of K   over QQ, such that vp(d(γ))=kvp(d(γ))=k. This set is completely determined for certain splitting types of p.VideoFor a video summary of this paper, please visit http://youtu.be/EagXNh_d9Xg.