The Hasse-Minkowski Theorem and its Application to Rational Points on Conics
- Title
- The Hasse-Minkowski Theorem and its Application to Rational Points on Conics
- Author
- 권영욱
- Advisor(s)
- 김창헌
- Issue Date
- 2013-08
- Publisher
- 한양대학교
- Degree
- Master
- Abstract
- In this thesis, we study the problem finding rational points on conics.
To solve this problem, we analyze the proof of the Hasse-Minkowski theorem, which relates the solutions of quadratic forms over rational numbers to the solutions over local fields. From the proof for the ternary case, we will see that given a rational quadratic form we only need to check the solvability over a finite number of local fields and that the local solvability is reduced to the solvability over a finite field. These facts will lead us to an algorithm which involves computations of Legendre symbols and systems of linear congruences. We will apply the algorithm to several examples.
- URI
- https://repository.hanyang.ac.kr/handle/20.500.11754/132632http://hanyang.dcollection.net/common/orgView/200000422301
- Appears in Collections:
- GRADUATE SCHOOL[S](대학원) > MATHEMATICS(수학과) > Theses (Master)
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