Polynomials with a given cyclic Galois group

Acta Mathematica Academiae Paedagogicae Nyíregyháziensis

Jiri Cihlar¹  Jaroslav Fuka¹  Martin Kuril¹ 

[1] J.E. Purkyne University

关键词: discriminant of a number field.;   

DOI  :  

学科分类：数学（综合）

来源: Academia Paedagogica Nyiregyhaziensis. Acta Mathematica

【 摘 要 】

For every natural number $n$ such that $2n+1$ is a prime, we present an explicit monic irreducible $n$th degree polynomial with integer coefficients whose Galois group over the field of all rational numbers is isomorphic to the cyclic group $Z_n$. The discriminant of the splitting field of the presented polynomial is equal to $(2n+1)^{n-1}$.

【 授权许可】

Unknown