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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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