Thesis (Selection of subject)Thesis (Selection of subject)(version: 354)
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Sums of squares in number fields
Thesis title in Czech: Součty čtverců v číselných tělesech
Thesis title in English: Sums of squares in number fields
Key words: kvadratická tělesa|součet čtverců|nerozložitelné prvky
English key words: quadratic fields|sum of squares|indecomposables
Academic year of topic announcement: 2020/2021
Type of assignment: Bachelor's thesis
Thesis language: angličtina
Department: Department of Algebra (32-KA)
Supervisor: doc. Mgr. Vítězslav Kala, Ph.D.
Author: hidden - assigned and confirmed by the Study Dept.
Date of registration: 27.10.2020
Date of assignment: 27.10.2020
Confirmed by Study dept. on: 23.11.2020
Date and time of defence: 08.07.2021 08:00
Date of electronic submission:27.05.2021
Date of submission of printed version:27.05.2021
Date of proceeded defence: 08.07.2021
Reviewers: Pavlo Yatsyna, Ph.D.
The goal of the thesis is to study which elements of totally real number fields are sums of squares. In the main real quadratic case, the student will build on the results of Peters and Kala-Yatsyna to study when all multiples of a given rational integer m are sums of squares. Further, the student may possibly focus on certain cubic fields, or on the related properties of indecomposable elements.
C. L. Siegel, Darstellung total positiver Zahlen durch Quadrate, Math. Z. 11 (1921), 246-275.
M. Peters, Quadratische Formen über Zahlringen, Acta Arith. 24 (1973), 157-164.
T. Hejda, V. Kala, Additive structure of totally positive quadratic integers, Manuscripta Math. 163 (2020), 263-278.
V. Kala, P. Yatsyna, Sums of squares in S-integers, New York J. Math. 26 (2020), 1145-1154.
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