Work

Bounds on the Pythagoras number and indecomposables in biquadratic fields

Year: 2025

Type: article

Abstract: We show that for all real biquadratic fields not containing $\sqrt{2}$ , $\sqrt{3}$ , $\sqrt{5}$ , $\sqrt{6}$ , $\sqrt{7}$ and $\sqrt{13}$ , the Pythagoras number of the ring of algebraic integers is at least 6. We also provide an upper bound on the norm and the minimal (codifferent) trace of additively indecomposable integers in some families of these fields.

Source: Proceedings of the Edinburgh Mathematical Society

DOI: 10.1017/s0013091525000112

Author: Magdaléna Tinková

Institutions: Charles University, Graz University of Technology, Czech Technical University in Prague

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Grantová Agentura České Republiky

Awards: Universal Quadratic Forms and Class Numbers, Local-global problems over number fields