n-univerzální kvadratické formy nad číselnými tělesy
| Thesis title in Czech: | n-univerzální kvadratické formy nad číselnými tělesy |
|---|---|
| Thesis title in English: | n-universal quadratic forms over number fields |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | dissertation |
| Thesis language: | |
| 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: | 01.09.2021 |
| Date of assignment: | 01.09.2021 |
| Confirmed by Study dept. on: | 14.09.2021 |
| Guidelines |
| A natural generalization of universal quadratic forms are n-universal forms, i.e., quadratic forms that represent all n-ary quadratic forms. The thesis aims to study the structure of n-universal forms over number fields and related concepts. In particular, indecomposable elements proved to be important for universal forms. In analogy with them, the student will investigate indecomposable n-ary forms and their relationship to n-universal forms. |
| References |
| O. T. O’Meara, Introduction to Quadratic Forms, Springer-Verlag, 1973.
V. Kala and P. Yatsyna, Lifting problem for universal quadratic forms, Adv. Math. 377(2021), 107497, 24 pp. J. S. Hsia, Y. Kitaoka, M. Kneser, Representations of positive definite quadratic forms, J. Reine Angew. Math. 301(1978), 132–141. L. J. Mordell, On the representation of a binary quadratic form as a sum of squares of linear forms, Math. Z. 35(1932), 1–15. H. Sasaki, Sums of squares of integral linear forms, J. Austral. Math. Soc. Ser. A69(2000), 298–302. C. Ko, Note on the representation of a quadratic form as a sum of squares of linear forms, Q. J. Math. 1(1937), 81–98. M. Čech, D. Lachman, J. Svoboda, M. Tinková, K. Zemková, Universal quadratic forms and indecomposables over biquadratic fields, Math. Nachr. 292, 540-555 (2019). |