Čebotarevova věta o hustotě a reálné kořeny polynomů
| Thesis title in Czech: | Čebotarevova věta o hustotě a reálné kořeny polynomů |
|---|---|
| Thesis title in English: | Chebotarev density theorem and real roots of polynomials |
| Academic year of topic announcement: | 2024/2025 |
| Thesis type: | Bachelor's thesis |
| 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: | 06.03.2025 |
| Date of assignment: | 06.03.2025 |
| Confirmed by Study dept. on: | 06.03.2025 |
| Advisors: | Subham Roy, Ph.D. |
| Guidelines |
| The Chebotarev density theorem links the classification of Galois extensions to the splitting behavior of primes. In this thesis, the student will carefully explain the necessary elements to formulate the Chebotarev density theorem and establish some applications of it. In particular, he will follow [AW] to work out the required details and conditions for polynomials having a real root under certain local conditions using the density theorem. |
| References |
| [AW] Angelo, R. and Xu, M. W. (2024): A polynomial with a root mod p for every p has a real root, https://arxiv.org/abs/2210.13735
[EM] Esmonde, J. and Murty, M. R. (1999): Problems in Algebraic Number Theory, Springer-Verlag [L] Lenstra, H: Lecture notes: The Chebotarev Density Theorem. https://websites.math.leidenuniv.nl/algebra/Lenstra-Chebotarev.pdf [M] Marcus, D. A. (1977): Number Fields, Springer International Publishing |