Reprezentace celistvých prvků pomocí forem vyššího stupně
| Thesis title in Czech: | Reprezentace celistvých prvků pomocí forem vyššího stupně |
|---|---|
| Thesis title in English: | Representations of algebraic integers by higher degree forms |
| Academic year of topic announcement: | 2022/2023 |
| 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: | 07.09.2023 |
| Date of assignment: | 07.09.2023 |
| Confirmed by Study dept. on: | 04.10.2023 |
| Guidelines |
| The last few decades saw exciting developments in the arithmetic theory of quadratic forms, including the 290-theorem over rational integers, as well as the study of ranks of universal forms over number fields using indecomposable integers. The goal of this thesis is to develop some of the analogous results for representations by forms (i.e., homogeneous polynomials) of higher degrees, and to consider their connections to other closely related topics, such as class numbers. |
| References |
| M. Bhargava, J. Hanke, Universal quadratic forms and the 290-theorem, preprint
D. K. Harrison, Grothendieck Ring of Higher Degree Forms, J. Algebra 35 (1975), 123-138 J. S. Hsia, Y. Kitaoka, M. Kneser, Representations of positive definite quadratic forms, J. Reine Angew. Math. 301 (1978), 132-141 V. Kala, Universal quadratic forms and indecomposables in number fields: A survey, arxiv:2301.13222 V. Kala, P. Yatsyna, Lifting problem for universal quadratic forms, Adv. Math. 377 (2021), 107497 O. T. O’Meara, Introduction to Quadratic Forms, Springer-Verlag, 1973 |