Aritmetika číselných těles: rozklady, normy a kvadratické formy
| Thesis title in Czech: | Aritmetika číselných těles: rozklady, normy a kvadratické formy |
|---|---|
| Thesis title in English: | Arithmetics of number fields: partitions, norms, and quadratic forms |
| 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: | 18.10.2021 |
| Guidelines |
| The student will investigate the arithmetics of number fields, especially in the totally real case. He will focus on sums of indecomposable integers and their use in estimates for the number of elements of bounded norm. He will also examine suitable families of number fields and their applications in the theory of universal quadratic forms. |
| References |
| [1] V. Blomer and A. Granville. Estimates for representation numbers of quadratic forms. Duke Math. J., 135(2):261-302, Nov. 2006.
[2] H. Iwaniec and E. Kowalski. Analytic number theory. American Mathematical Society, 2004. [3] V. Kala and M. Tinková. Universal quadratic forms, small norms and traces in families of number fields. Available at arXiv:2005.12312, 2020. [4] J. Neukirch. Algebraic Number Theory. Springer-Verlag Berlin Heidelberg, 1999. [5] C. L. Siegel. Berechnung von Zetafunktionen an ganzzahligen Stellen. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, 1969. |