Geodesic
Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$
Mathematica Bohemica, Tome 146 (2021) no. 4, pp. 471-481.

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If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prime of the form $4+n^2$, we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q{\mathcal O}_{K}$, where $q$ is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals.
DOI : 10.21136/MB.2021.0131-19
Classification : 11R16, 11S15
Keywords: ramification; cyclic quartic field; discriminant; index 
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Pérez-Hernández, Julio; Pineda-Ruelas, Mario. Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$. Mathematica Bohemica, Tome 146 (2021) no. 4, pp. 471-481. doi : 10.21136/MB.2021.0131-19. http://geodesic.mathdoc.fr/articles/10.21136/MB.2021.0131-19/

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