Sums of two integer squares in a certain quartic extension

Albertas Zinevičius

Address: Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius, LT – 03225, Lithuania

E-mail: albertas.zinevicius@mif.vu.lt

Abstract: An example of a quartic extension of the rational number field that does not have quadratic subfields and there exists a set of rational prime numbers $p \equiv 3 \pmod{4}$ of positive Dirichlet density such that either $p$ or $31p$ is a sum of two squares of integers of the extension is given.

AMSclassification: primary 11R37; secondary 11D09.

Keywords: Sums of two integer squares, quartic number field.

DOI: 10.5817/AM2026-2-69