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 |
| Thesis type: | 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 |
| Opponents: | Pavlo Yatsyna, Ph.D. |
| Guidelines |
| 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. |
| References |
| 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. |